TSTP Solution File: GRP127-4.004 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP127-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 11:45:41 EDT 2022
% Result : Unsatisfiable 0.21s 0.56s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP127-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 14 11:49:09 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.21/0.56
% 0.21/0.56 SPASS V 3.9
% 0.21/0.56 SPASS beiseite: Proof found.
% 0.21/0.56 % SZS status Theorem
% 0.21/0.56 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.56 SPASS derived 724 clauses, backtracked 132 clauses, performed 15 splits and kept 554 clauses.
% 0.21/0.56 SPASS allocated 76302 KBytes.
% 0.21/0.56 SPASS spent 0:00:00.18 on the problem.
% 0.21/0.56 0:00:00.03 for the input.
% 0.21/0.56 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.56 0:00:00.01 for inferences.
% 0.21/0.56 0:00:00.00 for the backtracking.
% 0.21/0.56 0:00:00.11 for the reduction.
% 0.21/0.56
% 0.21/0.56
% 0.21/0.56 Here is a proof with depth 15, length 149 :
% 0.21/0.56 % SZS output start Refutation
% 0.21/0.56 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)*.
% 0.21/0.56 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)*.
% 0.21/0.56 3[0:Inp] || -> group_element(e_1)*.
% 0.21/0.56 4[0:Inp] || -> group_element(e_2)*.
% 0.21/0.56 5[0:Inp] || -> group_element(e_3)*.
% 0.21/0.56 6[0:Inp] || -> group_element(e_4)*.
% 0.21/0.56 7[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.21/0.56 8[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.21/0.56 9[0:Inp] || equalish(e_1,e_4)*+ -> .
% 0.21/0.56 10[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.21/0.56 12[0:Inp] || equalish(e_2,e_4)*+ -> .
% 0.21/0.56 13[0:Inp] || equalish(e_3,e_1)*+ -> .
% 0.21/0.56 14[0:Inp] || equalish(e_3,e_2)*+ -> .
% 0.21/0.56 15[0:Inp] || equalish(e_3,e_4)*+ -> .
% 0.21/0.56 16[0:Inp] || equalish(e_4,e_1)*+ -> .
% 0.21/0.56 17[0:Inp] || equalish(e_4,e_2)*+ -> .
% 0.21/0.56 18[0:Inp] || equalish(e_4,e_3)*+ -> .
% 0.21/0.56 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)*.
% 0.21/0.56 20[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.21/0.56 21[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.21/0.56 22[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.21/0.56 23[0:Inp] || -> product(u,u,u)*.
% 0.21/0.56 24[0:Inp] || product(u,v,w)*+ product(w,v,x)* -> product(v,x,u)*.
% 0.21/0.56 25[0:Inp] || product(u,v,w)*+ product(x,u,v)* -> product(w,u,x)*.
% 0.21/0.56 26[0:Inp] || product(u,v,w)*+ product(v,x,u)* -> product(w,v,x)*.
% 0.21/0.56 39[0:Res:23.0,22.0] || product(u,v,v)*+ -> equalish(u,v).
% 0.21/0.56 43[0:Res:23.0,21.0] || product(u,v,u)*+ -> equalish(v,u).
% 0.21/0.56 45[0:Res:23.0,20.0] || product(u,u,v)*+ -> equalish(v,u).
% 0.21/0.56 53[0:Res:1.5,43.0] 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).
% 0.21/0.56 64[0:SSi:53.0,3.0] 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).
% 0.21/0.56 70[0:Res:64.3,45.0] 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).
% 0.21/0.56 81[0:SSi:70.0,4.0] || -> product(e_4,e_2,e_1) product(e_3,e_2,e_1)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.21/0.56 82[0:MRR:81.2,81.3,10.0,7.0] || -> product(e_4,e_2,e_1) product(e_3,e_2,e_1)*.
% 0.21/0.56 83[0:Res:82.1,24.0] || product(e_1,e_2,u)*+ -> product(e_4,e_2,e_1) product(e_2,u,e_3).
% 0.21/0.56 86[0:Res:82.1,20.0] || product(e_3,e_2,u)*+ -> product(e_4,e_2,e_1) equalish(u,e_1).
% 0.21/0.56 87[0:Res:82.1,21.0] || product(e_3,u,e_1)*+ -> product(e_4,e_2,e_1) equalish(u,e_2).
% 0.21/0.56 88[0:Res:82.1,22.0] || product(u,e_2,e_1)*+ -> product(e_4,e_2,e_1)* equalish(u,e_3).
% 0.21/0.56 109[1:Spt:86.0,86.2] || product(e_3,e_2,u)*+ -> equalish(u,e_1).
% 0.21/0.56 111[2:Spt:87.0,87.2] || product(e_3,u,e_1)*+ -> equalish(u,e_2).
% 0.21/0.56 112[2:Res:2.5,111.0] group_element(e_1) group_element(e_3) || -> product(e_3,e_4,e_1) product(e_3,e_3,e_1) product(e_3,e_2,e_1)* equalish(e_1,e_2).
% 0.21/0.56 114[2:SSi:112.1,112.0,5.0,3.0] || -> product(e_3,e_4,e_1) product(e_3,e_3,e_1) product(e_3,e_2,e_1)* equalish(e_1,e_2).
% 0.21/0.56 115[2:MRR:114.3,7.0] || -> product(e_3,e_4,e_1) product(e_3,e_3,e_1) product(e_3,e_2,e_1)*.
% 0.21/0.56 124[3:Spt:88.0,88.2] || product(u,e_2,e_1)*+ -> equalish(u,e_3).
% 0.21/0.56 154[4:Spt:83.1] || -> product(e_4,e_2,e_1)*.
% 0.21/0.56 161[4:Res:154.0,124.0] || -> equalish(e_4,e_3)*.
% 0.21/0.56 162[4:MRR:161.0,18.0] || -> .
% 0.21/0.56 163[4:Spt:162.0,83.1,154.0] || product(e_4,e_2,e_1)*+ -> .
% 0.21/0.56 164[4:Spt:162.0,83.0,83.2] || product(e_1,e_2,u)*+ -> product(e_2,u,e_3).
% 0.21/0.56 181[4:Res:19.5,163.0] 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)*.
% 0.21/0.56 182[4:SSi:181.1,181.0,6.0,4.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3) product(e_4,e_2,e_2)*.
% 0.21/0.56 185[4:Res:182.2,39.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.21/0.56 193[4:MRR:185.2,17.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3)*.
% 0.21/0.56 197[4:Res:193.1,20.0] || product(e_4,e_2,u)*+ -> product(e_4,e_2,e_4)* equalish(u,e_3).
% 0.21/0.56 199[4:Res:193.1,22.0] || product(u,e_2,e_3)*+ -> product(e_4,e_2,e_4)* equalish(u,e_4).
% 0.21/0.56 202[5:Spt:197.0,197.2] || product(e_4,e_2,u)*+ -> equalish(u,e_3).
% 0.21/0.56 233[6:Spt:199.0,199.2] || product(u,e_2,e_3)*+ -> equalish(u,e_4).
% 0.21/0.56 234[6:Res:1.5,233.0] group_element(e_3) group_element(e_2) || -> product(e_4,e_2,e_3) product(e_3,e_2,e_3) product(e_2,e_2,e_3)* equalish(e_1,e_4).
% 0.21/0.56 237[6:SSi:234.1,234.0,4.0,5.0] || -> product(e_4,e_2,e_3) product(e_3,e_2,e_3) product(e_2,e_2,e_3)* equalish(e_1,e_4).
% 0.21/0.56 238[6:MRR:237.3,9.0] || -> product(e_4,e_2,e_3) product(e_3,e_2,e_3) product(e_2,e_2,e_3)*.
% 0.21/0.56 239[7:Spt:238.0] || -> product(e_4,e_2,e_3)*.
% 0.21/0.56 241[7:Res:239.0,25.0] || product(u,e_4,e_2)*+ -> product(e_3,e_4,u)*.
% 0.21/0.56 290[7:Res:1.5,241.0] group_element(e_2) group_element(e_4) || -> product(e_4,e_4,e_2) product(e_3,e_4,e_2) product(e_2,e_4,e_2)* product(e_3,e_4,e_1).
% 0.21/0.56 291[7:SSi:290.1,290.0,6.0,4.0] || -> product(e_4,e_4,e_2) product(e_3,e_4,e_2) product(e_2,e_4,e_2)* product(e_3,e_4,e_1).
% 0.21/0.56 292[7:MRR:291.2,241.0] || -> product(e_4,e_4,e_2) product(e_3,e_4,e_2) product(e_3,e_4,e_1)*.
% 0.21/0.56 330[7:Res:292.2,111.0] || -> product(e_4,e_4,e_2) product(e_3,e_4,e_2)* equalish(e_4,e_2).
% 0.21/0.56 331[7:MRR:330.2,17.0] || -> product(e_4,e_4,e_2) product(e_3,e_4,e_2)*.
% 0.21/0.56 338[7:Res:331.1,241.0] || -> product(e_4,e_4,e_2) product(e_3,e_4,e_3)*.
% 0.21/0.56 341[8:Spt:338.0] || -> product(e_4,e_4,e_2)*.
% 0.21/0.56 342[8:Res:341.0,45.0] || -> equalish(e_2,e_4)*.
% 0.21/0.56 353[8:MRR:342.0,12.0] || -> .
% 0.21/0.56 354[8:Spt:353.0,338.0,341.0] || product(e_4,e_4,e_2)* -> .
% 0.21/0.56 355[8:Spt:353.0,338.1] || -> product(e_3,e_4,e_3)*.
% 0.21/0.56 363[8:Res:355.0,43.0] || -> equalish(e_4,e_3)*.
% 0.21/0.56 372[8:MRR:363.0,18.0] || -> .
% 0.21/0.56 373[7:Spt:372.0,238.0,239.0] || product(e_4,e_2,e_3)*+ -> .
% 0.21/0.56 374[7:Spt:372.0,238.1,238.2] || -> product(e_3,e_2,e_3) product(e_2,e_2,e_3)*.
% 0.21/0.56 375[7:MRR:193.1,373.0] || -> product(e_4,e_2,e_4)*.
% 0.21/0.56 400[7:Res:375.0,202.0] || -> equalish(e_4,e_3)*.
% 0.21/0.56 402[7:MRR:400.0,18.0] || -> .
% 0.21/0.56 403[6:Spt:402.0,199.1] || -> product(e_4,e_2,e_4)*.
% 0.21/0.56 413[6:Res:403.0,202.0] || -> equalish(e_4,e_3)*.
% 0.21/0.56 415[6:MRR:413.0,18.0] || -> .
% 0.21/0.56 416[5:Spt:415.0,197.1] || -> product(e_4,e_2,e_4)*.
% 0.21/0.56 417[5:Res:416.0,43.0] || -> equalish(e_2,e_4)*.
% 0.21/0.56 426[5:MRR:417.0,12.0] || -> .
% 0.21/0.56 427[3:Spt:426.0,88.1] || -> product(e_4,e_2,e_1)*.
% 0.21/0.56 433[3:Res:427.0,22.0] || product(u,e_2,e_1)*+ -> equalish(u,e_4).
% 0.21/0.56 468[4:Spt:115.0] || -> product(e_3,e_4,e_1)*.
% 0.21/0.56 477[4:Res:468.0,111.0] || -> equalish(e_4,e_2)*.
% 0.21/0.56 478[4:MRR:477.0,17.0] || -> .
% 0.21/0.56 479[4:Spt:478.0,115.0,468.0] || product(e_3,e_4,e_1)* -> .
% 0.21/0.56 480[4:Spt:478.0,115.1,115.2] || -> product(e_3,e_3,e_1) product(e_3,e_2,e_1)*.
% 0.21/0.56 485[5:Spt:480.0] || -> product(e_3,e_3,e_1)*.
% 0.21/0.56 497[5:Res:485.0,111.0] || -> equalish(e_3,e_2)*.
% 0.21/0.56 499[5:MRR:497.0,14.0] || -> .
% 0.21/0.56 500[5:Spt:499.0,480.0,485.0] || product(e_3,e_3,e_1)* -> .
% 0.21/0.56 501[5:Spt:499.0,480.1] || -> product(e_3,e_2,e_1)*.
% 0.21/0.56 516[5:Res:501.0,433.0] || -> equalish(e_3,e_4)*.
% 0.21/0.56 517[5:MRR:516.0,15.0] || -> .
% 0.21/0.56 518[2:Spt:517.0,87.1] || -> product(e_4,e_2,e_1)*.
% 0.21/0.56 519[2:Res:518.0,24.0] || product(e_1,e_2,u)*+ -> product(e_2,u,e_4).
% 0.21/0.56 522[2:Res:518.0,20.0] || product(e_4,e_2,u)*+ -> equalish(u,e_1).
% 0.21/0.56 550[2:Res:19.5,519.0] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,e_1,e_4).
% 0.21/0.56 551[2:SSi:550.1,550.0,3.0,4.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,e_1,e_4).
% 0.21/0.56 571[2:Res:551.2,39.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)* product(e_2,e_1,e_4) equalish(e_1,e_2).
% 0.21/0.56 584[2:MRR:571.3,7.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)* product(e_2,e_1,e_4).
% 0.21/0.56 596[2:Res:584.1,519.0] || -> product(e_1,e_2,e_4)* product(e_2,e_1,e_4) product(e_2,e_3,e_4).
% 0.21/0.56 613[3:Spt:596.0] || -> product(e_1,e_2,e_4)*.
% 0.21/0.56 624[3:Res:613.0,519.0] || -> product(e_2,e_4,e_4)*.
% 0.21/0.56 627[3:Res:624.0,39.0] || -> equalish(e_2,e_4)*.
% 0.21/0.56 638[3:MRR:627.0,12.0] || -> .
% 0.21/0.56 640[3:Spt:638.0,596.0,613.0] || product(e_1,e_2,e_4)*+ -> .
% 0.21/0.56 641[3:Spt:638.0,596.1,596.2] || -> product(e_2,e_1,e_4)* product(e_2,e_3,e_4).
% 0.21/0.56 722[3:Res:1.5,640.0] group_element(e_4) group_element(e_2) || -> product(e_4,e_2,e_4) product(e_3,e_2,e_4) product(e_2,e_2,e_4)*.
% 0.21/0.56 723[3:SSi:722.1,722.0,4.0,6.0] || -> product(e_4,e_2,e_4) product(e_3,e_2,e_4) product(e_2,e_2,e_4)*.
% 0.21/0.56 735[3:Res:723.2,45.0] || -> product(e_4,e_2,e_4) product(e_3,e_2,e_4)* equalish(e_4,e_2).
% 0.21/0.56 747[3:MRR:735.2,17.0] || -> product(e_4,e_2,e_4) product(e_3,e_2,e_4)*.
% 0.21/0.56 757[3:Res:747.1,109.0] || -> product(e_4,e_2,e_4)* equalish(e_4,e_1).
% 0.21/0.56 758[3:MRR:757.0,757.1,522.0,16.0] || -> .
% 0.21/0.56 760[1:Spt:758.0,86.1] || -> product(e_4,e_2,e_1)*.
% 0.21/0.56 761[1:Res:760.0,24.0] || product(e_1,e_2,u)*+ -> product(e_2,u,e_4).
% 0.21/0.56 763[1:Res:760.0,26.0] || product(e_2,u,e_4)+ -> product(e_1,e_2,u)*.
% 0.21/0.56 765[1:Res:760.0,21.0] || product(e_4,u,e_1)*+ -> equalish(u,e_2).
% 0.21/0.56 766[1:Res:760.0,22.0] || product(u,e_2,e_1)*+ -> equalish(u,e_4).
% 0.21/0.56 798[1:Res:19.5,761.0] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,e_1,e_4).
% 0.21/0.56 799[1:SSi:798.1,798.0,3.0,4.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3) product(e_1,e_2,e_2)* product(e_2,e_1,e_4).
% 0.21/0.56 805[1:Res:799.2,39.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)* product(e_2,e_1,e_4) equalish(e_1,e_2).
% 0.21/0.56 819[1:MRR:805.3,7.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)* product(e_2,e_1,e_4).
% 0.21/0.56 843[1:Res:819.1,761.0] || -> product(e_1,e_2,e_4)* product(e_2,e_1,e_4) product(e_2,e_3,e_4).
% 0.21/0.56 848[2:Spt:843.0] || -> product(e_1,e_2,e_4)*.
% 0.21/0.56 859[2:Res:848.0,761.0] || -> product(e_2,e_4,e_4)*.
% 0.21/0.56 863[2:Res:859.0,39.0] || -> equalish(e_2,e_4)*.
% 0.21/0.56 875[2:MRR:863.0,12.0] || -> .
% 0.21/0.56 877[2:Spt:875.0,843.0,848.0] || product(e_1,e_2,e_4)*+ -> .
% 0.21/0.56 878[2:Spt:875.0,843.1,843.2] || -> product(e_2,e_1,e_4)* product(e_2,e_3,e_4).
% 0.21/0.56 888[3:Spt:878.0] || -> product(e_2,e_1,e_4)*.
% 0.21/0.56 899[3:Res:888.0,763.0] || -> product(e_1,e_2,e_1)*.
% 0.21/0.56 921[3:Res:899.0,766.0] || -> equalish(e_1,e_4)*.
% 0.21/0.56 923[3:MRR:921.0,9.0] || -> .
% 0.21/0.56 932[3:Spt:923.0,878.0,888.0] || product(e_2,e_1,e_4)*+ -> .
% 0.21/0.56 933[3:Spt:923.0,878.1] || -> product(e_2,e_3,e_4)*.
% 0.21/0.56 946[3:Res:933.0,20.0] || product(e_2,e_3,u)*+ -> equalish(u,e_4).
% 0.21/0.56 1004[3:Res:64.3,946.0] group_element(e_3) || -> product(e_4,e_3,e_1) product(e_3,e_3,e_1)* equalish(e_3,e_1) equalish(e_1,e_4).
% 0.21/0.56 1007[3:SSi:1004.0,5.0] || -> product(e_4,e_3,e_1) product(e_3,e_3,e_1)* equalish(e_3,e_1) equalish(e_1,e_4).
% 0.21/0.56 1008[3:MRR:1007.2,1007.3,13.0,9.0] || -> product(e_4,e_3,e_1) product(e_3,e_3,e_1)*.
% 0.21/0.56 1009[3:Res:1008.1,45.0] || -> product(e_4,e_3,e_1)* equalish(e_1,e_3).
% 0.21/0.56 1023[3:MRR:1009.1,8.0] || -> product(e_4,e_3,e_1)*.
% 0.21/0.56 1045[3:Res:1023.0,765.0] || -> equalish(e_3,e_2)*.
% 0.21/0.56 1049[3:MRR:1045.0,14.0] || -> .
% 0.21/0.56 % SZS output end Refutation
% 0.21/0.56 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_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 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation product_idempotence qg3_1 qg3_2 qg3
% 0.21/0.56
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