TSTP Solution File: GRP127-1.004 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP127-1.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 11:45:39 EDT 2022
% Result : Unsatisfiable 0.19s 0.59s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP127-1.004 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 : Mon Jun 13 04:46:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.59
% 0.19/0.59 SPASS V 3.9
% 0.19/0.59 SPASS beiseite: Proof found.
% 0.19/0.59 % SZS status Theorem
% 0.19/0.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.59 SPASS derived 785 clauses, backtracked 129 clauses, performed 15 splits and kept 510 clauses.
% 0.19/0.59 SPASS allocated 76445 KBytes.
% 0.19/0.59 SPASS spent 0:00:00.25 on the problem.
% 0.19/0.59 0:00:00.03 for the input.
% 0.19/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.59 0:00:00.02 for inferences.
% 0.19/0.59 0:00:00.00 for the backtracking.
% 0.19/0.59 0:00:00.18 for the reduction.
% 0.19/0.59
% 0.19/0.59
% 0.19/0.59 Here is a proof with depth 16, length 134 :
% 0.19/0.59 % SZS output start Refutation
% 0.19/0.59 1[0:Inp] || -> group_element(e_1)*.
% 0.19/0.59 2[0:Inp] || -> group_element(e_2)*.
% 0.19/0.59 3[0:Inp] || -> group_element(e_3)*.
% 0.19/0.59 4[0:Inp] || -> group_element(e_4)*.
% 0.19/0.59 5[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.19/0.59 6[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.19/0.59 7[0:Inp] || equalish(e_1,e_4)*+ -> .
% 0.19/0.59 8[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.19/0.59 9[0:Inp] || equalish(e_2,e_3)*+ -> .
% 0.19/0.59 10[0:Inp] || equalish(e_2,e_4)*+ -> .
% 0.19/0.59 12[0:Inp] || equalish(e_3,e_2)*+ -> .
% 0.19/0.59 13[0:Inp] || equalish(e_3,e_4)*+ -> .
% 0.19/0.59 14[0:Inp] || equalish(e_4,e_1)*+ -> .
% 0.19/0.59 15[0:Inp] || equalish(e_4,e_2)*+ -> .
% 0.19/0.59 16[0:Inp] || equalish(e_4,e_3)*+ -> .
% 0.19/0.59 17[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)*.
% 0.19/0.59 18[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.19/0.59 19[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.19/0.59 20[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.19/0.59 21[0:Inp] || -> product(u,u,u)*.
% 0.19/0.59 22[0:Inp] || product(u,v,w)*+ product(v,x,u)* -> product(w,v,x)*.
% 0.19/0.59 24[0:Res:21.0,22.1] || product(u,v,u)*+ -> product(u,u,v)*.
% 0.19/0.59 31[0:Res:21.0,20.0] || product(u,v,v)*+ -> equalish(u,v).
% 0.19/0.59 33[0:Res:21.0,19.0] || product(u,v,u)*+ -> equalish(v,u).
% 0.19/0.59 38[0:Res:17.5,33.0] group_element(u) group_element(e_1) || -> product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 0.19/0.59 39[0:Res:17.5,24.0] group_element(u) group_element(e_1) || -> product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* product(e_1,e_1,u)*.
% 0.19/0.59 42[0:Res:17.5,22.0] group_element(u) group_element(v) || product(u,w,v)*+ -> product(v,u,e_4) product(v,u,e_3) product(v,u,e_2)* product(e_1,u,w)*.
% 0.19/0.59 46[0:Res:17.5,31.0] group_element(e_1) group_element(u) || -> product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(u,e_1).
% 0.19/0.59 47[0:SSi:46.0,1.0] group_element(u) || -> product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(u,e_1).
% 0.19/0.59 49[0:SSi:38.1,1.0] group_element(u) || -> product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 0.19/0.59 51[0:SSi:39.1,1.0] group_element(u) || -> product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* product(e_1,e_1,u)*.
% 0.19/0.59 52[0:Res:47.3,33.0] group_element(e_2) || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.19/0.59 60[0:SSi:52.0,2.0] || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.19/0.59 61[0:MRR:60.2,60.3,8.0,5.0] || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)*.
% 0.19/0.59 66[0:Res:61.1,22.0] || product(e_1,u,e_2)*+ -> product(e_2,e_1,e_4) product(e_3,e_1,u).
% 0.19/0.59 67[0:Res:61.1,18.0] || product(e_2,e_1,u)*+ -> product(e_2,e_1,e_4)* equalish(u,e_3).
% 0.19/0.59 70[1:Spt:67.0,67.2] || product(e_2,e_1,u)*+ -> equalish(u,e_3).
% 0.19/0.59 82[2:Spt:66.1] || -> product(e_2,e_1,e_4)*.
% 0.19/0.59 87[2:Res:82.0,70.0] || -> equalish(e_4,e_3)*.
% 0.19/0.59 88[2:MRR:87.0,16.0] || -> .
% 0.19/0.59 89[2:Spt:88.0,66.1,82.0] || product(e_2,e_1,e_4)*+ -> .
% 0.19/0.59 90[2:Spt:88.0,66.0,66.2] || product(e_1,u,e_2)*+ -> product(e_3,e_1,u).
% 0.19/0.59 91[2:MRR:61.0,89.0] || -> product(e_2,e_1,e_3)*.
% 0.19/0.59 106[0:Res:49.3,31.0] group_element(e_2) || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.19/0.59 108[0:SSi:106.0,2.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.19/0.59 109[0:MRR:108.2,108.3,8.0,5.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)*.
% 0.19/0.59 121[0:Res:109.1,19.0] || product(e_1,u,e_3)*+ -> product(e_1,e_2,e_4)* equalish(u,e_2).
% 0.19/0.59 122[0:Res:109.1,20.0] || product(u,e_2,e_3)*+ -> product(e_1,e_2,e_4)* equalish(u,e_1).
% 0.19/0.59 129[3:Spt:121.0,121.2] || product(e_1,u,e_3)*+ -> equalish(u,e_2).
% 0.19/0.59 137[2:Res:91.0,42.2] group_element(e_2) group_element(e_3) || -> product(e_3,e_2,e_4) product(e_3,e_2,e_3) product(e_3,e_2,e_2) product(e_1,e_2,e_1)*.
% 0.19/0.59 139[2:SSi:137.1,137.0,3.0,2.0] || -> product(e_3,e_2,e_4) product(e_3,e_2,e_3) product(e_3,e_2,e_2) product(e_1,e_2,e_1)*.
% 0.19/0.59 172[2:Res:139.3,33.0] || -> product(e_3,e_2,e_4) product(e_3,e_2,e_3) product(e_3,e_2,e_2)* equalish(e_2,e_1).
% 0.19/0.59 183[2:MRR:172.3,8.0] || -> product(e_3,e_2,e_4) product(e_3,e_2,e_3) product(e_3,e_2,e_2)*.
% 0.19/0.59 206[2:Res:183.2,31.0] || -> product(e_3,e_2,e_4) product(e_3,e_2,e_3)* equalish(e_3,e_2).
% 0.19/0.59 208[2:MRR:206.2,12.0] || -> product(e_3,e_2,e_4) product(e_3,e_2,e_3)*.
% 0.19/0.59 210[2:Res:208.1,33.0] || -> product(e_3,e_2,e_4)* equalish(e_2,e_3).
% 0.19/0.59 219[2:MRR:210.1,9.0] || -> product(e_3,e_2,e_4)*.
% 0.19/0.59 223[2:Res:219.0,22.0] || product(e_2,u,e_3)*+ -> product(e_4,e_2,u).
% 0.19/0.59 225[2:Res:219.0,19.0] || product(e_3,u,e_4)*+ -> equalish(u,e_2).
% 0.19/0.59 226[2:Res:219.0,20.0] || product(u,e_2,e_4)*+ -> equalish(u,e_3).
% 0.19/0.59 246[2:Res:91.0,223.0] || -> product(e_4,e_2,e_1)*.
% 0.19/0.59 247[2:Res:246.0,42.2] group_element(e_4) group_element(e_1) || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3) product(e_1,e_4,e_2)* product(e_1,e_4,e_2)*.
% 0.19/0.59 257[2:Obv:247.4] group_element(e_4) group_element(e_1) || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3) product(e_1,e_4,e_2)*.
% 0.19/0.59 258[2:SSi:257.1,257.0,1.0,4.0] || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3) product(e_1,e_4,e_2)*.
% 0.19/0.59 304[2:Res:258.2,90.0] || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3)* product(e_3,e_1,e_4).
% 0.19/0.59 307[4:Spt:304.0] || -> product(e_1,e_4,e_4)*.
% 0.19/0.59 313[4:Res:307.0,31.0] || -> equalish(e_1,e_4)*.
% 0.19/0.59 315[4:MRR:313.0,7.0] || -> .
% 0.19/0.59 317[4:Spt:315.0,304.0,307.0] || product(e_1,e_4,e_4)* -> .
% 0.19/0.59 318[4:Spt:315.0,304.1,304.2] || -> product(e_1,e_4,e_3)* product(e_3,e_1,e_4).
% 0.19/0.59 324[5:Spt:318.0] || -> product(e_1,e_4,e_3)*.
% 0.19/0.59 330[5:Res:324.0,129.0] || -> equalish(e_4,e_2)*.
% 0.19/0.59 332[5:MRR:330.0,15.0] || -> .
% 0.19/0.59 334[5:Spt:332.0,318.0,324.0] || product(e_1,e_4,e_3)* -> .
% 0.19/0.59 335[5:Spt:332.0,318.1] || -> product(e_3,e_1,e_4)*.
% 0.19/0.59 347[5:Res:335.0,225.0] || -> equalish(e_1,e_2)*.
% 0.19/0.59 348[5:MRR:347.0,5.0] || -> .
% 0.19/0.59 350[3:Spt:348.0,121.1] || -> product(e_1,e_2,e_4)*.
% 0.19/0.59 358[3:Res:350.0,226.0] || -> equalish(e_1,e_3)*.
% 0.19/0.59 360[3:MRR:358.0,6.0] || -> .
% 0.19/0.59 362[1:Spt:360.0,67.1] || -> product(e_2,e_1,e_4)*.
% 0.19/0.59 366[1:Res:362.0,42.2] 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) product(e_1,e_2,e_1)*.
% 0.19/0.59 367[1:Res:362.0,22.0] || product(e_1,u,e_2)*+ -> product(e_4,e_1,u).
% 0.19/0.59 370[1:Res:362.0,20.0] || product(u,e_1,e_4)*+ -> equalish(u,e_2).
% 0.19/0.59 374[1:SSi:366.1,366.0,4.0,2.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3) product(e_4,e_2,e_2) product(e_1,e_2,e_1)*.
% 0.19/0.59 375[2:Spt:109.0] || -> product(e_1,e_2,e_4)*.
% 0.19/0.59 379[2:Res:375.0,19.0] || product(e_1,u,e_4)*+ -> equalish(u,e_2).
% 0.19/0.59 380[2:Res:375.0,20.0] || product(u,e_2,e_4)*+ -> equalish(u,e_1).
% 0.19/0.59 414[1:Res:51.4,370.0] group_element(e_4) || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3) product(e_1,e_4,e_2)* equalish(e_1,e_2).
% 0.19/0.59 415[1:SSi:414.0,4.0] || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3) product(e_1,e_4,e_2)* equalish(e_1,e_2).
% 0.19/0.59 416[1:MRR:415.3,5.0] || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3) product(e_1,e_4,e_2)*.
% 0.19/0.59 471[1:Res:416.2,367.0] || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3)* product(e_4,e_1,e_4).
% 0.19/0.59 526[3:Spt:471.0] || -> product(e_1,e_4,e_4)*.
% 0.19/0.59 533[3:Res:526.0,379.0] || -> equalish(e_4,e_2)*.
% 0.19/0.59 536[3:MRR:533.0,15.0] || -> .
% 0.19/0.59 538[3:Spt:536.0,471.0,526.0] || product(e_1,e_4,e_4)*+ -> .
% 0.19/0.59 539[3:Spt:536.0,471.1,471.2] || -> product(e_1,e_4,e_3)* product(e_4,e_1,e_4).
% 0.19/0.59 545[4:Spt:539.0] || -> product(e_1,e_4,e_3)*.
% 0.19/0.59 549[4:Res:545.0,19.0] || product(e_1,u,e_3)*+ -> equalish(u,e_4).
% 0.19/0.59 561[4:Res:51.4,549.0] group_element(e_3) || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* equalish(e_1,e_4).
% 0.19/0.59 564[4:SSi:561.0,3.0] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)* equalish(e_1,e_4).
% 0.19/0.59 565[4:MRR:564.3,7.0] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3) product(e_1,e_3,e_2)*.
% 0.19/0.59 624[4:Res:565.2,367.0] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3)* product(e_4,e_1,e_3).
% 0.19/0.59 627[5:Spt:624.0] || -> product(e_1,e_3,e_4)*.
% 0.19/0.59 633[5:Res:627.0,379.0] || -> equalish(e_3,e_2)*.
% 0.44/0.60 635[5:MRR:633.0,12.0] || -> .
% 0.44/0.60 637[5:Spt:635.0,624.0,627.0] || product(e_1,e_3,e_4)*+ -> .
% 0.44/0.60 638[5:Spt:635.0,624.1,624.2] || -> product(e_1,e_3,e_3)* product(e_4,e_1,e_3).
% 0.44/0.60 644[6:Spt:638.0] || -> product(e_1,e_3,e_3)*.
% 0.44/0.60 651[6:Res:644.0,549.0] || -> equalish(e_3,e_4)*.
% 0.44/0.60 654[6:MRR:651.0,13.0] || -> .
% 0.44/0.60 656[6:Spt:654.0,638.0,644.0] || product(e_1,e_3,e_3)*+ -> .
% 0.44/0.60 657[6:Spt:654.0,638.1] || -> product(e_4,e_1,e_3)*.
% 0.44/0.60 666[6:Res:657.0,19.0] || product(e_4,u,e_3)*+ -> equalish(u,e_1).
% 0.44/0.60 884[1:Res:374.3,33.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3) product(e_4,e_2,e_2)* equalish(e_2,e_1).
% 0.44/0.60 895[6:MRR:884.1,884.3,666.0,8.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_2)*.
% 0.44/0.60 933[6:Res:895.1,31.0] || -> product(e_4,e_2,e_4)* equalish(e_4,e_2).
% 0.44/0.60 935[6:MRR:933.1,15.0] || -> product(e_4,e_2,e_4)*.
% 0.44/0.60 945[6:Res:935.0,380.0] || -> equalish(e_4,e_1)*.
% 0.44/0.60 947[6:MRR:945.0,14.0] || -> .
% 0.44/0.60 950[4:Spt:947.0,539.0,545.0] || product(e_1,e_4,e_3)* -> .
% 0.44/0.60 951[4:Spt:947.0,539.1] || -> product(e_4,e_1,e_4)*.
% 0.44/0.60 957[1:MRR:884.3,8.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3) product(e_4,e_2,e_2)*.
% 0.44/0.60 966[4:Res:951.0,370.0] || -> equalish(e_4,e_2)*.
% 0.44/0.60 969[4:MRR:966.0,15.0] || -> .
% 0.44/0.60 979[2:Spt:969.0,109.0,375.0] || product(e_1,e_2,e_4)*+ -> .
% 0.44/0.60 980[2:Spt:969.0,109.1] || -> product(e_1,e_2,e_3)*.
% 0.44/0.60 981[2:MRR:122.1,979.0] || product(u,e_2,e_3)*+ -> equalish(u,e_1).
% 0.44/0.60 1055[1:Res:957.2,31.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.44/0.60 1057[1:MRR:1055.2,15.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3)*.
% 0.44/0.60 1097[2:Res:1057.1,981.0] || -> product(e_4,e_2,e_4)* equalish(e_4,e_1).
% 0.44/0.60 1098[2:MRR:1097.1,14.0] || -> product(e_4,e_2,e_4)*.
% 0.44/0.60 1100[2:Res:1098.0,33.0] || -> equalish(e_2,e_4)*.
% 0.44/0.60 1108[2:MRR:1100.0,10.0] || -> .
% 0.44/0.60 % SZS output end Refutation
% 0.44/0.60 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_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
% 0.44/0.60
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