TSTP Solution File: GRP124-4.004 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP124-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 11:45:31 EDT 2022
% Result : Unsatisfiable 0.45s 0.60s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP124-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 07:40:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.45/0.60
% 0.45/0.60 SPASS V 3.9
% 0.45/0.60 SPASS beiseite: Proof found.
% 0.45/0.60 % SZS status Theorem
% 0.45/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.60 SPASS derived 998 clauses, backtracked 202 clauses, performed 19 splits and kept 791 clauses.
% 0.45/0.60 SPASS allocated 76433 KBytes.
% 0.45/0.60 SPASS spent 0:00:00.27 on the problem.
% 0.45/0.60 0:00:00.03 for the input.
% 0.45/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.45/0.60 0:00:00.01 for inferences.
% 0.45/0.60 0:00:00.00 for the backtracking.
% 0.45/0.60 0:00:00.19 for the reduction.
% 0.45/0.60
% 0.45/0.60
% 0.45/0.60 Here is a proof with depth 11, length 139 :
% 0.45/0.60 % SZS output start Refutation
% 0.45/0.60 1[0:Inp] group_element(u) group_element(v) || -> product(e_4,v,u) product(e_3,v,u) product(e_2,v,u) product(e_1,v,u)*.
% 0.45/0.60 2[0:Inp] group_element(u) group_element(v) || -> product(v,e_4,u) product(v,e_3,u) product(v,e_2,u) product(v,e_1,u)*.
% 0.45/0.60 3[0:Inp] || -> group_element(e_1)*.
% 0.45/0.60 4[0:Inp] || -> group_element(e_2)*.
% 0.45/0.60 5[0:Inp] || -> group_element(e_3)*.
% 0.45/0.60 6[0:Inp] || -> group_element(e_4)*.
% 0.45/0.60 7[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.45/0.60 8[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.45/0.60 9[0:Inp] || equalish(e_1,e_4)*+ -> .
% 0.45/0.60 10[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.45/0.60 11[0:Inp] || equalish(e_2,e_3)*+ -> .
% 0.45/0.60 12[0:Inp] || equalish(e_2,e_4)*+ -> .
% 0.45/0.60 13[0:Inp] || equalish(e_3,e_1)*+ -> .
% 0.45/0.60 15[0:Inp] || equalish(e_3,e_4)*+ -> .
% 0.45/0.60 16[0:Inp] || equalish(e_4,e_1)*+ -> .
% 0.45/0.60 17[0:Inp] || equalish(e_4,e_2)*+ -> .
% 0.45/0.60 18[0:Inp] || equalish(e_4,e_3)*+ -> .
% 0.45/0.60 19[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_4) product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 0.45/0.60 20[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.45/0.60 21[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.45/0.60 22[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.45/0.60 23[0:Inp] || -> product(u,u,u)*.
% 0.45/0.60 24[0:Inp] || product(u,v,w)*+ product(u,x,y)* product(v,w,z)* product(x,y,z)* -> equalish(x,v)*.
% 0.45/0.60 43[0:Res:23.0,24.1] || product(u,v,v)*+ product(u,w,x)* product(w,x,v)* -> equalish(w,v).
% 0.45/0.60 62[0:Res:23.0,22.0] || product(u,v,v)*+ -> equalish(u,v).
% 0.45/0.60 64[0:Res:23.0,21.0] || product(u,v,u)*+ -> equalish(v,u).
% 0.45/0.60 66[0:Res:23.0,20.0] || product(u,u,v)*+ -> equalish(v,u).
% 0.45/0.60 68[0:Res:1.5,66.0] group_element(u) group_element(e_1) || -> product(e_4,e_1,u) product(e_3,e_1,u) product(e_2,e_1,u)* equalish(u,e_1).
% 0.45/0.60 73[0:Res:1.5,64.0] group_element(e_1) group_element(u) || -> product(e_4,u,e_1) product(e_3,u,e_1) product(e_2,u,e_1)* equalish(u,e_1).
% 0.45/0.60 74[0:SSi:73.0,3.0] group_element(u) || -> product(e_4,u,e_1) product(e_3,u,e_1) product(e_2,u,e_1)* equalish(u,e_1).
% 0.45/0.60 76[0:SSi:68.1,3.0] group_element(u) || -> product(e_4,e_1,u) product(e_3,e_1,u) product(e_2,e_1,u)* equalish(u,e_1).
% 0.45/0.60 77[0:Res:74.3,66.0] group_element(e_2) || -> product(e_4,e_2,e_1) product(e_3,e_2,e_1)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.45/0.60 82[0:SSi:77.0,4.0] || -> product(e_4,e_2,e_1) product(e_3,e_2,e_1)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.45/0.60 83[0:MRR:82.2,82.3,10.0,7.0] || -> product(e_4,e_2,e_1) product(e_3,e_2,e_1)*.
% 0.45/0.60 85[0:Res:83.1,21.0] || product(e_3,u,e_1)*+ -> product(e_4,e_2,e_1) equalish(u,e_2).
% 0.45/0.60 86[0:Res:83.1,22.0] || product(u,e_2,e_1)*+ -> product(e_4,e_2,e_1)* equalish(u,e_3).
% 0.45/0.60 89[1:Spt:85.0,85.2] || product(e_3,u,e_1)*+ -> equalish(u,e_2).
% 0.45/0.60 95[0:Res:2.5,62.0] group_element(e_1) group_element(u) || -> product(u,e_4,e_1) product(u,e_3,e_1) product(u,e_2,e_1)* equalish(u,e_1).
% 0.45/0.60 101[0:SSi:95.0,3.0] group_element(u) || -> product(u,e_4,e_1) product(u,e_3,e_1) product(u,e_2,e_1)* equalish(u,e_1).
% 0.45/0.60 108[2:Spt:86.0,86.2] || product(u,e_2,e_1)*+ -> equalish(u,e_3).
% 0.45/0.60 117[0:Res:76.3,64.0] group_element(e_2) || -> product(e_4,e_1,e_2) product(e_3,e_1,e_2)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.45/0.60 118[0:SSi:117.0,4.0] || -> product(e_4,e_1,e_2) product(e_3,e_1,e_2)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.45/0.60 119[0:MRR:118.2,118.3,10.0,7.0] || -> product(e_4,e_1,e_2) product(e_3,e_1,e_2)*.
% 0.45/0.60 120[0:Res:119.1,20.0] || product(e_3,e_1,u)*+ -> product(e_4,e_1,e_2) equalish(u,e_2).
% 0.45/0.60 151[0:Res:101.3,66.0] group_element(e_2) || -> product(e_2,e_4,e_1) product(e_2,e_3,e_1)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.45/0.60 159[0:SSi:151.0,4.0] || -> product(e_2,e_4,e_1) product(e_2,e_3,e_1)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.45/0.60 160[0:MRR:159.2,159.3,10.0,7.0] || -> product(e_2,e_4,e_1) product(e_2,e_3,e_1)*.
% 0.45/0.60 172[0:Res:160.1,20.0] || product(e_2,e_3,u)*+ -> product(e_2,e_4,e_1) equalish(u,e_1).
% 0.45/0.60 257[0:Res:23.0,43.0] || product(u,v,w)*+ product(v,w,u)* -> equalish(v,u).
% 0.45/0.60 452[3:Spt:83.0] || -> product(e_4,e_2,e_1)*.
% 0.45/0.60 461[3:Res:452.0,108.0] || -> equalish(e_4,e_3)*.
% 0.45/0.60 462[3:MRR:461.0,18.0] || -> .
% 0.45/0.60 467[3:Spt:462.0,83.0,452.0] || product(e_4,e_2,e_1)*+ -> .
% 0.45/0.60 468[3:Spt:462.0,83.1] || -> product(e_3,e_2,e_1)*.
% 0.45/0.60 473[3:Res:468.0,257.0] || product(e_2,e_1,e_3)* -> equalish(e_2,e_3).
% 0.45/0.60 482[3:MRR:473.1,11.0] || product(e_2,e_1,e_3)*+ -> .
% 0.45/0.60 485[3:Res:19.5,467.0] group_element(e_2) group_element(e_4) || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3) product(e_4,e_2,e_2)*.
% 0.45/0.60 488[3:SSi:485.1,485.0,6.0,4.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3) product(e_4,e_2,e_2)*.
% 0.45/0.60 490[3:Res:76.3,482.0] group_element(e_3) || -> product(e_4,e_1,e_3) product(e_3,e_1,e_3)* equalish(e_3,e_1).
% 0.45/0.60 491[3:SSi:490.0,5.0] || -> product(e_4,e_1,e_3) product(e_3,e_1,e_3)* equalish(e_3,e_1).
% 0.45/0.60 492[3:MRR:491.2,13.0] || -> product(e_4,e_1,e_3) product(e_3,e_1,e_3)*.
% 0.45/0.60 504[3:Res:488.2,62.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.45/0.60 505[3:MRR:504.2,17.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3)*.
% 0.45/0.60 524[3:Res:492.1,64.0] || -> product(e_4,e_1,e_3)* equalish(e_1,e_3).
% 0.45/0.60 526[3:MRR:524.1,8.0] || -> product(e_4,e_1,e_3)*.
% 0.45/0.60 529[3:Res:526.0,257.0] || product(e_1,e_3,e_4)* -> equalish(e_1,e_4).
% 0.45/0.60 535[3:MRR:529.1,9.0] || product(e_1,e_3,e_4)*+ -> .
% 0.45/0.60 537[3:Res:1.5,535.0] group_element(e_4) group_element(e_3) || -> product(e_4,e_3,e_4) product(e_3,e_3,e_4) product(e_2,e_3,e_4)*.
% 0.45/0.60 538[3:SSi:537.1,537.0,5.0,6.0] || -> product(e_4,e_3,e_4) product(e_3,e_3,e_4) product(e_2,e_3,e_4)*.
% 0.45/0.60 556[3:Res:505.1,257.0] || product(e_2,e_3,e_4)* -> product(e_4,e_2,e_4) equalish(e_2,e_4).
% 0.45/0.60 562[3:MRR:556.1,556.2,64.0,12.0] || product(e_2,e_3,e_4)*+ -> .
% 0.45/0.60 563[3:MRR:538.2,562.0] || -> product(e_4,e_3,e_4) product(e_3,e_3,e_4)*.
% 0.45/0.60 565[3:Res:563.1,66.0] || -> product(e_4,e_3,e_4)* equalish(e_4,e_3).
% 0.45/0.60 575[3:MRR:565.1,18.0] || -> product(e_4,e_3,e_4)*.
% 0.45/0.60 585[3:Res:575.0,64.0] || -> equalish(e_3,e_4)*.
% 0.45/0.60 586[3:MRR:585.0,15.0] || -> .
% 0.45/0.60 587[2:Spt:586.0,86.1] || -> product(e_4,e_2,e_1)*.
% 0.45/0.60 591[2:Res:587.0,257.0] || product(e_2,e_1,e_4)* -> equalish(e_2,e_4).
% 0.45/0.60 595[2:Res:587.0,21.0] || product(e_4,u,e_1)*+ -> equalish(u,e_2).
% 0.45/0.60 597[2:MRR:591.1,12.0] || product(e_2,e_1,e_4)*+ -> .
% 0.45/0.60 610[2:Res:76.3,597.0] group_element(e_4) || -> product(e_4,e_1,e_4) product(e_3,e_1,e_4)* equalish(e_4,e_1).
% 0.45/0.60 611[2:SSi:610.0,6.0] || -> product(e_4,e_1,e_4) product(e_3,e_1,e_4)* equalish(e_4,e_1).
% 0.45/0.60 612[2:MRR:611.2,16.0] || -> product(e_4,e_1,e_4) product(e_3,e_1,e_4)*.
% 0.45/0.60 614[3:Spt:160.0] || -> product(e_2,e_4,e_1)*.
% 0.45/0.60 619[3:Res:614.0,257.0] || product(e_4,e_1,e_2)* -> equalish(e_4,e_2).
% 0.45/0.60 625[3:MRR:619.1,17.0] || product(e_4,e_1,e_2)*+ -> .
% 0.45/0.60 630[3:MRR:120.1,625.0] || product(e_3,e_1,u)*+ -> equalish(u,e_2).
% 0.45/0.60 732[3:Res:612.1,630.0] || -> product(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.45/0.60 734[3:MRR:732.1,17.0] || -> product(e_4,e_1,e_4)*.
% 0.45/0.60 748[3:Res:734.0,64.0] || -> equalish(e_1,e_4)*.
% 0.45/0.60 749[3:MRR:748.0,9.0] || -> .
% 0.45/0.60 750[3:Spt:749.0,160.0,614.0] || product(e_2,e_4,e_1)*+ -> .
% 0.45/0.60 751[3:Spt:749.0,160.1] || -> product(e_2,e_3,e_1)*.
% 0.45/0.60 774[3:Res:74.3,750.0] group_element(e_4) || -> product(e_4,e_4,e_1) product(e_3,e_4,e_1)* equalish(e_4,e_1).
% 0.45/0.60 776[3:SSi:774.0,6.0] || -> product(e_4,e_4,e_1) product(e_3,e_4,e_1)* equalish(e_4,e_1).
% 0.45/0.60 777[3:MRR:776.2,16.0] || -> product(e_4,e_4,e_1) product(e_3,e_4,e_1)*.
% 0.45/0.60 797[4:Spt:612.0] || -> product(e_4,e_1,e_4)*.
% 0.45/0.60 810[4:Res:797.0,64.0] || -> equalish(e_1,e_4)*.
% 0.45/0.60 811[4:MRR:810.0,9.0] || -> .
% 0.45/0.60 812[4:Spt:811.0,612.0,797.0] || product(e_4,e_1,e_4)*+ -> .
% 0.45/0.60 813[4:Spt:811.0,612.1] || -> product(e_3,e_1,e_4)*.
% 0.45/0.60 839[5:Spt:777.0] || -> product(e_4,e_4,e_1)*.
% 0.45/0.60 854[5:Res:839.0,595.0] || -> equalish(e_4,e_2)*.
% 0.45/0.60 856[5:MRR:854.0,17.0] || -> .
% 0.45/0.60 858[5:Spt:856.0,777.0,839.0] || product(e_4,e_4,e_1)* -> .
% 0.45/0.60 859[5:Spt:856.0,777.1] || -> product(e_3,e_4,e_1)*.
% 0.45/0.60 873[5:Res:859.0,89.0] || -> equalish(e_4,e_2)*.
% 0.45/0.60 874[5:MRR:873.0,17.0] || -> .
% 0.45/0.60 877[1:Spt:874.0,85.1] || -> product(e_4,e_2,e_1)*.
% 0.45/0.61 884[1:Res:877.0,257.0] || product(e_2,e_1,e_4)* -> equalish(e_2,e_4).
% 0.45/0.61 890[1:MRR:884.1,12.0] || product(e_2,e_1,e_4)*+ -> .
% 0.45/0.61 893[1:Res:2.5,890.0] group_element(e_4) group_element(e_2) || -> product(e_2,e_4,e_4) product(e_2,e_3,e_4) product(e_2,e_2,e_4)*.
% 0.45/0.61 894[1:Res:76.3,890.0] group_element(e_4) || -> product(e_4,e_1,e_4) product(e_3,e_1,e_4)* equalish(e_4,e_1).
% 0.45/0.61 895[1:SSi:894.0,6.0] || -> product(e_4,e_1,e_4) product(e_3,e_1,e_4)* equalish(e_4,e_1).
% 0.45/0.61 896[1:MRR:895.2,16.0] || -> product(e_4,e_1,e_4) product(e_3,e_1,e_4)*.
% 0.45/0.61 897[1:SSi:893.1,893.0,4.0,6.0] || -> product(e_2,e_4,e_4) product(e_2,e_3,e_4) product(e_2,e_2,e_4)*.
% 0.45/0.61 898[2:Spt:119.0] || -> product(e_4,e_1,e_2)*.
% 0.45/0.61 923[3:Spt:160.0] || -> product(e_2,e_4,e_1)*.
% 0.45/0.61 930[3:Res:923.0,257.0] || product(e_4,e_1,e_2)* -> equalish(e_4,e_2).
% 0.45/0.61 938[3:MRR:930.0,930.1,898.0,17.0] || -> .
% 0.45/0.61 940[3:Spt:938.0,160.0,923.0] || product(e_2,e_4,e_1)*+ -> .
% 0.45/0.61 941[3:Spt:938.0,160.1] || -> product(e_2,e_3,e_1)*.
% 0.45/0.61 945[3:MRR:172.1,940.0] || product(e_2,e_3,u)*+ -> equalish(u,e_1).
% 0.45/0.61 1122[4:Spt:897.0] || -> product(e_2,e_4,e_4)*.
% 0.45/0.61 1137[4:Res:1122.0,62.0] || -> equalish(e_2,e_4)*.
% 0.45/0.61 1141[4:MRR:1137.0,12.0] || -> .
% 0.45/0.61 1146[4:Spt:1141.0,897.0,1122.0] || product(e_2,e_4,e_4)*+ -> .
% 0.45/0.61 1147[4:Spt:1141.0,897.1,897.2] || -> product(e_2,e_3,e_4) product(e_2,e_2,e_4)*.
% 0.45/0.61 1161[4:Res:1147.1,66.0] || -> product(e_2,e_3,e_4)* equalish(e_4,e_2).
% 0.45/0.61 1176[4:MRR:1161.1,17.0] || -> product(e_2,e_3,e_4)*.
% 0.45/0.61 1206[4:Res:1176.0,945.0] || -> equalish(e_4,e_1)*.
% 0.45/0.61 1207[4:MRR:1206.0,16.0] || -> .
% 0.45/0.61 1213[2:Spt:1207.0,119.0,898.0] || product(e_4,e_1,e_2)*+ -> .
% 0.45/0.61 1214[2:Spt:1207.0,119.1] || -> product(e_3,e_1,e_2)*.
% 0.45/0.61 1217[2:MRR:120.1,1213.0] || product(e_3,e_1,u)*+ -> equalish(u,e_2).
% 0.45/0.61 1297[2:Res:896.1,1217.0] || -> product(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.45/0.61 1299[2:MRR:1297.1,17.0] || -> product(e_4,e_1,e_4)*.
% 0.45/0.61 1313[2:Res:1299.0,64.0] || -> equalish(e_1,e_4)*.
% 0.45/0.61 1314[2:MRR:1313.0,9.0] || -> .
% 0.45/0.61 % SZS output end Refutation
% 0.45/0.61 Formulae used in the proof : row_surjectivity column_surjectivity 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_4 e_4_is_not_e_1 e_4_is_not_e_2 e_4_is_not_e_3 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation product_idempotence qg2_1
% 0.45/0.61
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