TSTP Solution File: GRP132-1.002 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP132-1.002 : 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 11:45:49 EDT 2022
% Result : Unsatisfiable 0.91s 1.11s
% Output : Refutation 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GRP132-1.002 : TPTP v8.1.0. Released v1.2.0.
% 0.02/0.10 % Command : run_spass %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Mon Jun 13 12:11:41 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.91/1.11
% 0.91/1.11 SPASS V 3.9
% 0.91/1.11 SPASS beiseite: Proof found.
% 0.91/1.11 % SZS status Theorem
% 0.91/1.11 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.91/1.11 SPASS derived 2181 clauses, backtracked 600 clauses, performed 19 splits and kept 1393 clauses.
% 0.91/1.11 SPASS allocated 78555 KBytes.
% 0.91/1.11 SPASS spent 0:00:00.81 on the problem.
% 0.91/1.11 0:00:00.03 for the input.
% 0.91/1.11 0:00:00.00 for the FLOTTER CNF translation.
% 0.91/1.11 0:00:00.03 for inferences.
% 0.91/1.11 0:00:00.01 for the backtracking.
% 0.91/1.11 0:00:00.72 for the reduction.
% 0.91/1.11
% 0.91/1.11
% 0.91/1.11 Here is a proof with depth 12, length 175 :
% 0.91/1.11 % SZS output start Refutation
% 0.91/1.11 1[0:Inp] || -> group_element(e_1)*.
% 0.91/1.11 2[0:Inp] || -> group_element(e_2)*.
% 0.91/1.11 3[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.91/1.11 4[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.91/1.11 5[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_2) product(v,u,e_1)*.
% 0.91/1.11 6[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.91/1.11 7[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.91/1.11 8[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.91/1.11 9[0:Inp] || product(u,v,w)*+ product(u,x,y)* product(v,w,z)* product(x,y,z)* -> equalish(x,v)*.
% 0.91/1.11 10[0:Inp] || product(u,v,w)*+ product(u,x,y)* product(v,w,z)* product(x,y,z)* -> equalish(y,w)*.
% 0.91/1.11 14[0:Res:9.4,3.0] || product(u,e_2,v)*+ product(u,e_1,w)* product(e_2,v,x)* product(e_1,w,x)* -> .
% 0.91/1.11 17[0:Res:5.3,6.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_2)* equalish(w,e_1).
% 0.91/1.11 18[0:Res:5.3,7.0] group_element(u) group_element(v) || product(v,w,e_1)*+ -> product(v,u,e_2)* equalish(w,u)*.
% 0.91/1.11 19[0:Res:5.3,8.0] group_element(u) group_element(v) || product(w,u,e_1)*+ -> product(v,u,e_2)* equalish(w,v)*.
% 0.91/1.11 20[0:Res:5.3,17.2] group_element(u) group_element(v) group_element(u) group_element(v) || -> product(v,u,e_2)* product(v,u,e_2)* equalish(e_1,e_1).
% 0.91/1.11 21[0:Obv:20.4] group_element(u) group_element(v) || -> product(v,u,e_2)* equalish(e_1,e_1).
% 0.91/1.11 22[0:Res:5.3,10.0] group_element(u) group_element(v) || product(v,w,x)*+ product(u,e_1,y)* product(w,x,y)* -> product(v,u,e_2)* equalish(x,e_1).
% 0.91/1.11 23[1:Spt:21.0,21.1,21.2] group_element(u) group_element(v) || -> product(v,u,e_2)*.
% 0.91/1.11 26[1:Res:23.2,7.0] group_element(u) group_element(v) || product(v,w,e_2)*+ -> equalish(w,u)*.
% 0.91/1.11 34[1:Res:23.2,26.2] group_element(u) group_element(v) group_element(w) group_element(v) || -> equalish(u,w)*.
% 0.91/1.11 35[1:Obv:34.1] group_element(u) group_element(v) group_element(w) || -> equalish(u,v)*.
% 0.91/1.11 36[1:Con:35.2] group_element(u) group_element(v) || -> equalish(u,v)*.
% 0.91/1.11 38[1:Res:36.2,3.0] group_element(e_1) group_element(e_2) || -> .
% 0.91/1.11 40[1:SSi:38.1,38.0,2.0,1.0] || -> .
% 0.91/1.11 41[1:Spt:40.0,21.3] || -> equalish(e_1,e_1)*.
% 0.91/1.11 42[0:Res:5.3,9.0] group_element(u) group_element(v) || product(v,w,x)*+ product(u,e_1,y)* product(w,x,y)* -> product(v,u,e_2)* equalish(w,u)*.
% 0.91/1.11 49[0:Res:5.3,18.2] group_element(u) group_element(v) group_element(w) group_element(v) || -> product(v,u,e_2)* product(v,w,e_2)* equalish(u,w)*.
% 0.91/1.11 50[0:Obv:49.1] group_element(u) group_element(v) group_element(w) || -> product(w,u,e_2)* product(w,v,e_2)* equalish(u,v)*.
% 0.91/1.11 51[0:Res:5.3,19.2] group_element(u) group_element(v) group_element(u) group_element(w) || -> product(v,u,e_2)* product(w,u,e_2)* equalish(v,w)*.
% 0.91/1.11 52[0:Obv:51.0] group_element(u) group_element(v) group_element(w) || -> product(u,v,e_2)* product(w,v,e_2)* equalish(u,w)*.
% 0.91/1.11 53[0:Res:5.3,14.0] group_element(e_2) group_element(u) || product(u,e_1,v)* product(e_2,e_1,w) product(e_1,v,w)* -> product(u,e_2,e_2).
% 0.91/1.11 54[0:SSi:53.0,2.0] group_element(u) || product(u,e_1,v)*+ product(e_2,e_1,w) product(e_1,v,w)* -> product(u,e_2,e_2).
% 0.91/1.11 55[0:Fac:50.3,50.4] group_element(u) group_element(u) group_element(v) || -> product(v,u,e_2)* equalish(u,u)*.
% 0.91/1.11 72[0:Obv:55.0] group_element(u) group_element(v) || -> product(v,u,e_2)* equalish(u,u)*.
% 0.91/1.11 92[0:Res:72.2,14.0] group_element(e_2) group_element(u) || product(u,e_1,v)* product(e_2,e_2,w) product(e_1,v,w)* -> equalish(e_2,e_2).
% 0.91/1.11 96[0:SSi:92.0,2.0] group_element(u) || product(u,e_1,v)*+ product(e_2,e_2,w) product(e_1,v,w)* -> equalish(e_2,e_2).
% 0.91/1.11 139[0:Res:50.3,42.2] group_element(u) group_element(v) group_element(w) group_element(x) group_element(w) || product(x,e_1,y)* product(u,e_2,y)* -> product(w,v,e_2)* equalish(u,v)* product(w,x,e_2)* equalish(u,x)*.
% 0.91/1.11 145[0:Obv:139.2] group_element(u) group_element(v) group_element(w) group_element(x) || product(w,e_1,y)* product(u,e_2,y)* -> product(x,v,e_2)* equalish(u,v)* product(x,w,e_2)* equalish(u,w)*.
% 0.91/1.11 146[0:Con:145.1] group_element(u) group_element(v) group_element(w) || product(v,e_1,x)*+ product(u,e_2,x)* -> product(w,v,e_2)* equalish(u,v)*.
% 0.91/1.11 149[0:Res:5.3,96.1] group_element(e_1) group_element(u) group_element(u) || product(e_2,e_2,v) product(e_1,e_1,v)* -> product(u,e_1,e_2)* equalish(e_2,e_2).
% 0.91/1.11 153[0:Obv:149.1] group_element(e_1) group_element(u) || product(e_2,e_2,v) product(e_1,e_1,v)* -> product(u,e_1,e_2)* equalish(e_2,e_2).
% 0.91/1.11 154[0:SSi:153.0,1.0] group_element(u) || product(e_2,e_2,v)+ product(e_1,e_1,v)* -> product(u,e_1,e_2)* equalish(e_2,e_2).
% 0.91/1.11 162[2:Spt:154.0,154.3] group_element(u) || -> product(u,e_1,e_2)*.
% 0.91/1.11 167[2:Res:162.1,8.0] group_element(u) || product(v,e_1,e_2)*+ -> equalish(v,u)*.
% 0.91/1.11 196[0:Res:5.3,54.1] group_element(e_1) group_element(u) group_element(u) || product(e_2,e_1,v) product(e_1,e_1,v)* -> product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.91/1.11 201[0:Obv:196.1] group_element(e_1) group_element(u) || product(e_2,e_1,v) product(e_1,e_1,v)* -> product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.91/1.11 218[2:Res:162.1,167.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 0.91/1.11 224[2:Res:218.2,3.0] group_element(e_1) group_element(e_2) || -> .
% 0.91/1.11 226[2:SSi:224.1,224.0,2.0,1.0] || -> .
% 0.91/1.11 227[2:Spt:226.0,154.1,154.2,154.4] || product(e_2,e_2,u)+ product(e_1,e_1,u)* -> equalish(e_2,e_2).
% 0.91/1.11 228[0:SSi:201.0,1.0] group_element(u) || product(e_2,e_1,v)+ product(e_1,e_1,v)* -> product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.91/1.11 309[0:Res:5.3,228.1] group_element(e_1) group_element(e_2) group_element(u) || product(e_1,e_1,e_1)* -> product(e_2,e_1,e_2) product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.91/1.11 313[0:SSi:309.1,309.0,2.0,1.0] group_element(u) || product(e_1,e_1,e_1)*+ -> product(e_2,e_1,e_2) product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.91/1.11 318[3:Spt:313.0,313.3,313.4] group_element(u) || -> product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.91/1.11 321[3:Res:318.1,6.0] group_element(u) || product(u,e_1,v)*+ -> product(u,e_2,e_2) equalish(v,e_2).
% 0.91/1.11 325[3:Res:318.1,54.1] group_element(u) group_element(u) || product(e_2,e_1,v) product(e_1,e_2,v)* -> product(u,e_2,e_2)* product(u,e_2,e_2)*.
% 0.91/1.11 332[3:Obv:325.4] group_element(u) || product(e_2,e_1,v)+ product(e_1,e_2,v)* -> product(u,e_2,e_2)*.
% 0.91/1.11 337[3:Res:318.1,321.1] group_element(u) group_element(u) || -> product(u,e_2,e_2)* product(u,e_2,e_2)* equalish(e_2,e_2).
% 0.91/1.11 342[3:Obv:337.2] group_element(u) || -> product(u,e_2,e_2)* equalish(e_2,e_2).
% 0.91/1.11 364[4:Spt:342.0,342.1] group_element(u) || -> product(u,e_2,e_2)*.
% 0.91/1.11 369[4:Res:364.1,8.0] group_element(u) || product(v,e_2,e_2)*+ -> equalish(v,u)*.
% 0.91/1.11 419[4:Res:364.1,369.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 0.91/1.11 425[4:Res:419.2,3.0] group_element(e_1) group_element(e_2) || -> .
% 0.91/1.11 427[4:SSi:425.1,425.0,2.0,1.0] || -> .
% 0.91/1.11 428[4:Spt:427.0,342.2] || -> equalish(e_2,e_2)*.
% 0.91/1.11 489[3:Res:318.1,332.1] group_element(e_2) group_element(u) || product(e_1,e_2,e_2)* -> product(e_2,e_2,e_2) product(u,e_2,e_2)*.
% 0.91/1.11 490[3:Res:5.3,332.1] group_element(e_1) group_element(e_2) group_element(u) || product(e_1,e_2,e_1)* -> product(e_2,e_1,e_2) product(u,e_2,e_2)*.
% 0.91/1.11 493[3:Con:489.1] group_element(e_2) || product(e_1,e_2,e_2)* -> product(e_2,e_2,e_2).
% 0.91/1.11 494[3:SSi:493.0,2.0] || product(e_1,e_2,e_2)*+ -> product(e_2,e_2,e_2).
% 0.91/1.11 495[3:SSi:490.1,490.0,2.0,1.0] group_element(u) || product(e_1,e_2,e_1)*+ -> product(e_2,e_1,e_2) product(u,e_2,e_2)*.
% 0.91/1.11 543[3:Res:50.3,494.0] group_element(e_2) group_element(u) group_element(e_1) || -> product(e_1,u,e_2)* equalish(e_2,u) product(e_2,e_2,e_2).
% 0.91/1.11 544[3:Res:52.4,494.0] group_element(u) group_element(e_2) group_element(e_1) || -> product(u,e_2,e_2)* equalish(u,e_1) product(e_2,e_2,e_2)*.
% 0.91/1.11 545[3:Res:50.4,494.0] group_element(u) group_element(e_2) group_element(e_1) || -> product(e_1,u,e_2)* equalish(u,e_2) product(e_2,e_2,e_2).
% 0.91/1.11 546[3:SSi:545.2,545.1,1.0,2.0] group_element(u) || -> product(e_1,u,e_2)* equalish(u,e_2) product(e_2,e_2,e_2).
% 1.06/1.27 547[3:SSi:544.2,544.1,1.0,2.0] group_element(u) || -> product(u,e_2,e_2)* equalish(u,e_1) product(e_2,e_2,e_2)*.
% 1.06/1.27 548[3:SSi:543.2,543.0,1.0,2.0] group_element(u) || -> product(e_1,u,e_2)* equalish(e_2,u) product(e_2,e_2,e_2).
% 1.06/1.27 550[5:Spt:546.0,546.1,546.2] group_element(u) || -> product(e_1,u,e_2)* equalish(u,e_2).
% 1.06/1.27 555[5:Res:550.1,8.0] group_element(u) || product(v,u,e_2)*+ -> equalish(u,e_2) equalish(v,e_1).
% 1.06/1.27 605[6:Spt:547.0,547.1,547.2] group_element(u) || -> product(u,e_2,e_2)* equalish(u,e_1).
% 1.06/1.27 623[7:Spt:548.0,548.1,548.2] group_element(u) || -> product(e_1,u,e_2)* equalish(e_2,u).
% 1.06/1.27 627[7:Res:623.1,7.0] group_element(u) || product(e_1,v,e_2)*+ -> equalish(e_2,u)* equalish(v,u)*.
% 1.06/1.27 702[5:Res:318.1,555.1] group_element(u) group_element(e_1) || -> product(u,e_2,e_2)* equalish(e_1,e_2) equalish(u,e_1).
% 1.06/1.27 1019[8:Spt:495.0,495.3] group_element(u) || -> product(u,e_2,e_2)*.
% 1.06/1.27 1045[8:Res:1019.1,627.1] group_element(e_1) group_element(u) || -> equalish(e_2,u)* equalish(e_2,u)*.
% 1.06/1.27 1061[8:Obv:1045.2] group_element(e_1) group_element(u) || -> equalish(e_2,u)*.
% 1.06/1.27 1062[8:SSi:1061.0,1.0] group_element(u) || -> equalish(e_2,u)*.
% 1.06/1.27 1093[8:Res:1062.1,4.0] group_element(e_1) || -> .
% 1.06/1.27 1094[8:SSi:1093.0,1.0] || -> .
% 1.06/1.27 1095[8:Spt:1094.0,495.1,495.2] || product(e_1,e_2,e_1)*+ -> product(e_2,e_1,e_2).
% 1.06/1.27 1096[8:Res:5.3,1095.0] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_2)* product(e_2,e_1,e_2).
% 1.06/1.27 1097[8:SSi:1096.1,1096.0,1.0,2.0] || -> product(e_1,e_2,e_2)* product(e_2,e_1,e_2).
% 1.06/1.27 1110[9:Spt:1097.1] || -> product(e_2,e_1,e_2)*.
% 1.06/1.27 1118[9:Res:1110.0,555.1] group_element(e_1) || -> equalish(e_1,e_2)* equalish(e_2,e_1).
% 1.06/1.27 1130[9:SSi:1118.0,1.0] || -> equalish(e_1,e_2)* equalish(e_2,e_1).
% 1.06/1.27 1131[9:MRR:1130.0,1130.1,3.0,4.0] || -> .
% 1.06/1.27 1138[9:Spt:1131.0,1097.1,1110.0] || product(e_2,e_1,e_2)*+ -> .
% 1.06/1.27 1139[9:Spt:1131.0,1097.0] || -> product(e_1,e_2,e_2)*.
% 1.06/1.27 1149[9:Res:1139.0,7.0] || product(e_1,u,e_2)* -> equalish(u,e_2).
% 1.06/1.27 1165[9:MRR:550.1,1149.0] group_element(u) || -> equalish(u,e_2)*.
% 1.06/1.27 1230[9:Res:1165.1,3.0] group_element(e_1) || -> .
% 1.06/1.27 1231[9:SSi:1230.0,1.0] || -> .
% 1.06/1.27 1232[7:Spt:1231.0,548.3] || -> product(e_2,e_2,e_2)*.
% 1.06/1.27 1239[7:Res:1232.0,7.0] || product(e_2,u,e_2)*+ -> equalish(u,e_2).
% 1.06/1.27 1697[5:Res:550.1,146.3] group_element(e_1) group_element(u) group_element(e_1) group_element(v) || product(u,e_2,e_2)* -> equalish(e_1,e_2) product(v,e_1,e_2)* equalish(u,e_1).
% 1.06/1.27 1699[5:Obv:1697.0] group_element(u) group_element(e_1) group_element(v) || product(u,e_2,e_2)* -> equalish(e_1,e_2) product(v,e_1,e_2)* equalish(u,e_1).
% 1.06/1.27 1700[5:SSi:1699.1,1.0] group_element(u) group_element(v) || product(u,e_2,e_2)* -> equalish(e_1,e_2) product(v,e_1,e_2)* equalish(u,e_1).
% 1.06/1.27 1701[6:MRR:1700.2,1700.3,605.1,3.0] group_element(u) group_element(v) || -> product(v,e_1,e_2)* equalish(u,e_1)*.
% 1.06/1.27 1710[8:Spt:1701.0,1701.3] group_element(u) || -> equalish(u,e_1)*.
% 1.06/1.27 1711[8:Res:1710.1,4.0] group_element(e_2) || -> .
% 1.06/1.27 1712[8:SSi:1711.0,2.0] || -> .
% 1.06/1.27 1713[8:Spt:1712.0,1701.1,1701.2] group_element(u) || -> product(u,e_1,e_2)*.
% 1.06/1.27 1735[8:Res:1713.1,1239.0] group_element(e_2) || -> equalish(e_1,e_2)*.
% 1.06/1.27 1746[8:SSi:1735.0,2.0] || -> equalish(e_1,e_2)*.
% 1.06/1.27 1747[8:MRR:1746.0,3.0] || -> .
% 1.06/1.27 1773[6:Spt:1747.0,547.3] || -> product(e_2,e_2,e_2)*.
% 1.06/1.27 1774[5:SSi:702.1,1.0] group_element(u) || -> product(u,e_2,e_2)* equalish(e_1,e_2) equalish(u,e_1).
% 1.06/1.27 1775[5:MRR:1774.2,3.0] group_element(u) || -> product(u,e_2,e_2)* equalish(u,e_1).
% 1.06/1.27 1776[5:MRR:1700.3,3.0] group_element(u) group_element(v) || product(u,e_2,e_2)* -> product(v,e_1,e_2)* equalish(u,e_1).
% 1.06/1.27 1777[5:MRR:1776.2,1775.1] group_element(u) group_element(v) || -> product(v,e_1,e_2)* equalish(u,e_1)*.
% 1.06/1.27 1782[6:Res:1773.0,7.0] || product(e_2,u,e_2)*+ -> equalish(u,e_2).
% 1.06/1.27 2005[7:Spt:1777.0,1777.3] group_element(u) || -> equalish(u,e_1)*.
% 1.06/1.27 2006[7:Res:2005.1,4.0] group_element(e_2) || -> .
% 1.06/1.27 2007[7:SSi:2006.0,2.0] || -> .
% 1.06/1.27 2008[7:Spt:2007.0,1777.1,1777.2] group_element(u) || -> product(u,e_1,e_2)*.
% 1.06/1.27 2029[7:Res:2008.1,1782.0] group_element(e_2) || -> equalish(e_1,e_2)*.
% 1.06/1.27 2038[7:SSi:2029.0,2.0] || -> equalish(e_1,e_2)*.
% 1.06/1.27 2039[7:MRR:2038.0,3.0] || -> .
% 1.06/1.27 2063[5:Spt:2039.0,546.3] || -> product(e_2,e_2,e_2)*.
% 1.06/1.27 2067[5:Res:2063.0,7.0] || product(e_2,u,e_2)*+ -> equalish(u,e_2).
% 1.06/1.27 2068[5:Res:2063.0,8.0] || product(u,e_2,e_2)*+ -> equalish(u,e_2).
% 1.06/1.27 2239[6:Spt:495.0,495.3] group_element(u) || -> product(u,e_2,e_2)*.
% 1.06/1.27 2260[6:Res:2239.1,2068.0] group_element(u) || -> equalish(u,e_2)*.
% 1.06/1.27 2277[6:Res:2260.1,3.0] group_element(e_1) || -> .
% 1.06/1.27 2278[6:SSi:2277.0,1.0] || -> .
% 1.06/1.27 2279[6:Spt:2278.0,495.1,495.2] || product(e_1,e_2,e_1)*+ -> product(e_2,e_1,e_2).
% 1.06/1.27 2280[6:Res:5.3,2279.0] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_2)* product(e_2,e_1,e_2).
% 1.06/1.27 2281[6:SSi:2280.1,2280.0,1.0,2.0] || -> product(e_1,e_2,e_2)* product(e_2,e_1,e_2).
% 1.06/1.27 2282[7:Spt:2281.1] || -> product(e_2,e_1,e_2)*.
% 1.06/1.27 2295[7:Res:2282.0,2067.0] || -> equalish(e_1,e_2)*.
% 1.06/1.27 2303[7:MRR:2295.0,3.0] || -> .
% 1.06/1.27 2316[7:Spt:2303.0,2281.1,2282.0] || product(e_2,e_1,e_2)* -> .
% 1.06/1.27 2317[7:Spt:2303.0,2281.0] || -> product(e_1,e_2,e_2)*.
% 1.06/1.27 2341[7:Res:2317.0,2068.0] || -> equalish(e_1,e_2)*.
% 1.06/1.27 2343[7:MRR:2341.0,3.0] || -> .
% 1.06/1.27 2352[3:Spt:2343.0,313.1,313.2] || product(e_1,e_1,e_1)*+ -> product(e_2,e_1,e_2).
% 1.06/1.27 2366[3:Res:5.3,2352.0] group_element(e_1) group_element(e_1) || -> product(e_1,e_1,e_2)* product(e_2,e_1,e_2).
% 1.06/1.27 2367[3:Obv:2366.0] group_element(e_1) || -> product(e_1,e_1,e_2)* product(e_2,e_1,e_2).
% 1.06/1.27 2368[3:SSi:2367.0,1.0] || -> product(e_1,e_1,e_2)* product(e_2,e_1,e_2).
% 1.06/1.27 2369[4:Spt:2368.1] || -> product(e_2,e_1,e_2)*.
% 1.06/1.27 2373[4:Res:2369.0,7.0] || product(e_2,u,e_2)*+ -> equalish(u,e_1).
% 1.06/1.27 2379[4:Res:2369.0,22.2] group_element(u) group_element(e_2) || product(u,e_1,v)* product(e_1,e_2,v)* -> product(e_2,u,e_2)* equalish(e_2,e_1).
% 1.06/1.27 2396[4:SSi:2379.1,2.0] group_element(u) || product(u,e_1,v)* product(e_1,e_2,v)* -> product(e_2,u,e_2)* equalish(e_2,e_1).
% 1.06/1.27 2397[4:MRR:2396.4,4.0] group_element(u) || product(u,e_1,v)*+ product(e_1,e_2,v)* -> product(e_2,u,e_2)*.
% 1.06/1.27 2473[4:Res:52.4,2373.0] group_element(u) group_element(v) group_element(e_2) || -> product(u,v,e_2)* equalish(u,e_2) equalish(v,e_1).
% 1.06/1.27 2477[4:SSi:2473.2,2.0] group_element(u) group_element(v) || -> product(u,v,e_2)* equalish(u,e_2) equalish(v,e_1).
% 1.06/1.27 3223[4:Res:2369.0,2397.1] group_element(e_2) || product(e_1,e_2,e_2)* -> product(e_2,e_2,e_2).
% 1.06/1.27 3230[4:SSi:3223.0,2.0] || product(e_1,e_2,e_2)*+ -> product(e_2,e_2,e_2).
% 1.06/1.27 3251[4:Res:2477.2,3230.0] group_element(e_1) group_element(e_2) || -> equalish(e_1,e_2) equalish(e_2,e_1) product(e_2,e_2,e_2)*.
% 1.06/1.27 3259[4:SSi:3251.1,3251.0,2.0,1.0] || -> equalish(e_1,e_2) equalish(e_2,e_1) product(e_2,e_2,e_2)*.
% 1.06/1.27 3260[4:MRR:3259.0,3259.1,3.0,4.0] || -> product(e_2,e_2,e_2)*.
% 1.06/1.27 3285[4:Res:3260.0,2373.0] || -> equalish(e_2,e_1)*.
% 1.06/1.27 3286[4:MRR:3285.0,4.0] || -> .
% 1.06/1.27 3301[4:Spt:3286.0,2368.1,2369.0] || product(e_2,e_1,e_2)*+ -> .
% 1.06/1.27 3302[4:Spt:3286.0,2368.0] || -> product(e_1,e_1,e_2)*.
% 1.06/1.27 3317[4:Res:3302.0,7.0] || product(e_1,u,e_2)*+ -> equalish(u,e_1).
% 1.06/1.27 3321[4:Res:3302.0,54.1] group_element(e_1) || product(e_2,e_1,u) product(e_1,e_2,u)* -> product(e_1,e_2,e_2)*.
% 1.06/1.27 3338[4:SSi:3321.0,1.0] || product(e_2,e_1,u)+ product(e_1,e_2,u)* -> product(e_1,e_2,e_2)*.
% 1.06/1.27 3586[4:Res:5.3,3338.0] group_element(e_1) group_element(e_2) || product(e_1,e_2,e_1)* -> product(e_2,e_1,e_2) product(e_1,e_2,e_2).
% 1.06/1.27 3594[4:SSi:3586.1,3586.0,2.0,1.0] || product(e_1,e_2,e_1)* -> product(e_2,e_1,e_2) product(e_1,e_2,e_2).
% 1.06/1.27 3595[4:MRR:3594.1,3301.0] || product(e_1,e_2,e_1)*+ -> product(e_1,e_2,e_2).
% 1.06/1.27 3596[4:Res:5.3,3595.0] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_2)* product(e_1,e_2,e_2)*.
% 1.06/1.27 3597[4:Obv:3596.2] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_2)*.
% 1.06/1.27 3598[4:SSi:3597.1,3597.0,1.0,2.0] || -> product(e_1,e_2,e_2)*.
% 1.06/1.27 3621[4:Res:3598.0,3317.0] || -> equalish(e_2,e_1)*.
% 1.06/1.27 3622[4:MRR:3621.0,4.0] || -> .
% 1.06/1.27 % SZS output end Refutation
% 1.06/1.27 Formulae used in the proof : element_1 element_2 e_1_is_not_e_2 e_2_is_not_e_1 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation qg2_1 qg2_2
% 1.06/1.27
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