TSTP Solution File: GRP126-4.004 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP126-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:45:38 EDT 2022
% Result : Unsatisfiable 0.52s 0.69s
% Output : Refutation 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP126-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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 : Tue Jun 14 12:07:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.52/0.69
% 0.52/0.69 SPASS V 3.9
% 0.52/0.69 SPASS beiseite: Proof found.
% 0.52/0.69 % SZS status Theorem
% 0.52/0.69 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.52/0.69 SPASS derived 1437 clauses, backtracked 183 clauses, performed 22 splits and kept 984 clauses.
% 0.52/0.69 SPASS allocated 77020 KBytes.
% 0.52/0.69 SPASS spent 0:00:00.35 on the problem.
% 0.52/0.69 0:00:00.03 for the input.
% 0.52/0.69 0:00:00.00 for the FLOTTER CNF translation.
% 0.52/0.69 0:00:00.02 for inferences.
% 0.52/0.69 0:00:00.01 for the backtracking.
% 0.52/0.69 0:00:00.26 for the reduction.
% 0.52/0.69
% 0.52/0.69
% 0.52/0.69 Here is a proof with depth 18, length 209 :
% 0.52/0.69 % SZS output start Refutation
% 0.52/0.69 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)*.
% 0.52/0.69 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)*.
% 0.52/0.69 3[0:Inp] || -> group_element(e_1)*.
% 0.52/0.69 4[0:Inp] || -> group_element(e_2)*.
% 0.52/0.69 5[0:Inp] || -> group_element(e_3)*.
% 0.52/0.69 6[0:Inp] || -> group_element(e_4)*.
% 0.52/0.69 7[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.52/0.69 8[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.52/0.69 9[0:Inp] || equalish(e_1,e_4)*+ -> .
% 0.52/0.69 10[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.52/0.69 12[0:Inp] || equalish(e_2,e_4)*+ -> .
% 0.52/0.69 13[0:Inp] || equalish(e_3,e_1)*+ -> .
% 0.52/0.69 14[0:Inp] || equalish(e_3,e_2)*+ -> .
% 0.52/0.69 15[0:Inp] || equalish(e_3,e_4)*+ -> .
% 0.52/0.69 16[0:Inp] || equalish(e_4,e_1)*+ -> .
% 0.52/0.69 17[0:Inp] || equalish(e_4,e_2)*+ -> .
% 0.52/0.69 18[0:Inp] || equalish(e_4,e_3)*+ -> .
% 0.52/0.69 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)*.
% 0.52/0.69 20[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.52/0.69 21[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.52/0.69 22[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.52/0.69 23[0:Inp] || -> product(u,u,u)*.
% 0.52/0.69 24[0:Inp] || product(u,v,w)*+ product(x,w,u)* -> product(v,u,x)*.
% 0.52/0.69 25[0:Inp] || product(u,v,w)*+ product(w,x,v)* -> product(v,u,x)*.
% 0.52/0.69 26[0:Inp] || product(u,v,w)*+ product(v,u,x)* -> product(x,w,u)*.
% 0.52/0.69 39[0:Res:23.0,22.0] || product(u,v,v)*+ -> equalish(u,v).
% 0.52/0.69 43[0:Res:23.0,21.0] || product(u,v,u)*+ -> equalish(v,u).
% 0.52/0.69 47[0:Res:23.0,20.0] || product(u,u,v)*+ -> equalish(v,u).
% 0.52/0.69 52[0:Res:1.5,47.0] 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).
% 0.52/0.69 58[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).
% 0.52/0.69 67[0:SSi:58.0,3.0] 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).
% 0.52/0.69 69[0:SSi:52.1,3.0] 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).
% 0.52/0.69 76[0:Res:2.5,47.0] group_element(u) group_element(e_1) || -> product(e_1,e_4,u) product(e_1,e_3,u) product(e_1,e_2,u)* equalish(u,e_1).
% 0.52/0.69 93[0:SSi:76.1,3.0] group_element(u) || -> product(e_1,e_4,u) product(e_1,e_3,u) product(e_1,e_2,u)* equalish(u,e_1).
% 0.52/0.69 100[0:Res:67.3,47.0] 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).
% 0.52/0.69 112[0:SSi:100.0,4.0] || -> product(e_4,e_2,e_1) product(e_3,e_2,e_1)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.52/0.69 113[0:MRR:112.2,112.3,10.0,7.0] || -> product(e_4,e_2,e_1) product(e_3,e_2,e_1)*.
% 0.52/0.69 114[0:Res:113.1,24.0] || product(u,e_1,e_3)*+ -> product(e_4,e_2,e_1) product(e_2,e_3,u)*.
% 0.52/0.69 116[0:Res:113.1,26.0] || product(e_2,e_3,u)* -> product(e_4,e_2,e_1) product(u,e_1,e_3)*.
% 0.52/0.69 117[0:Res:113.1,20.0] || product(e_3,e_2,u)*+ -> product(e_4,e_2,e_1) equalish(u,e_1).
% 0.52/0.69 118[0:Res:113.1,21.0] || product(e_3,u,e_1)*+ -> product(e_4,e_2,e_1) equalish(u,e_2).
% 0.52/0.69 119[0:Res:113.1,22.0] || product(u,e_2,e_1)*+ -> product(e_4,e_2,e_1)* equalish(u,e_3).
% 0.52/0.69 120[1:Spt:117.0,117.2] || product(e_3,e_2,u)*+ -> equalish(u,e_1).
% 0.52/0.69 122[2:Spt:118.0,118.2] || product(e_3,u,e_1)*+ -> equalish(u,e_2).
% 0.52/0.69 123[2:Res:2.5,122.0] 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).
% 0.52/0.69 125[2:SSi:123.1,123.0,5.0,3.0] || -> 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).
% 0.52/0.69 126[2:MRR:125.3,7.0] || -> product(e_3,e_4,e_1) product(e_3,e_3,e_1) product(e_3,e_2,e_1)*.
% 0.52/0.69 131[0:Res:19.5,39.0] 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).
% 0.52/0.69 146[0:SSi:131.0,3.0] 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).
% 0.52/0.69 162[3:Spt:119.0,119.2] || product(u,e_2,e_1)*+ -> equalish(u,e_3).
% 0.52/0.69 169[4:Spt:114.1] || -> product(e_4,e_2,e_1)*.
% 0.52/0.69 176[4:Res:169.0,162.0] || -> equalish(e_4,e_3)*.
% 0.52/0.69 177[4:MRR:176.0,18.0] || -> .
% 0.52/0.69 178[4:Spt:177.0,114.1,169.0] || product(e_4,e_2,e_1)*+ -> .
% 0.52/0.69 179[4:Spt:177.0,114.0,114.2] || product(u,e_1,e_3)*+ -> product(e_2,e_3,u)*.
% 0.52/0.69 182[4:MRR:116.1,178.0] || product(e_2,e_3,u)*+ -> product(u,e_1,e_3)*.
% 0.52/0.69 196[4:Res:19.5,178.0] 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)*.
% 0.52/0.69 197[4:SSi:196.1,196.0,6.0,4.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3) product(e_4,e_2,e_2)*.
% 0.52/0.69 202[4:Res:67.3,182.0] group_element(e_3) || -> product(e_4,e_3,e_1) product(e_3,e_3,e_1) equalish(e_3,e_1) product(e_1,e_1,e_3)*.
% 0.52/0.69 204[4:SSi:202.0,5.0] || -> product(e_4,e_3,e_1) product(e_3,e_3,e_1) equalish(e_3,e_1) product(e_1,e_1,e_3)*.
% 0.52/0.69 205[4:MRR:204.2,13.0] || -> product(e_4,e_3,e_1) product(e_3,e_3,e_1) product(e_1,e_1,e_3)*.
% 0.52/0.69 208[4:Res:197.2,39.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.52/0.69 216[4:MRR:208.2,17.0] || -> product(e_4,e_2,e_4) product(e_4,e_2,e_3)*.
% 0.52/0.69 220[4:Res:216.1,20.0] || product(e_4,e_2,u)*+ -> product(e_4,e_2,e_4)* equalish(u,e_3).
% 0.52/0.69 222[4:Res:216.1,22.0] || product(u,e_2,e_3)*+ -> product(e_4,e_2,e_4)* equalish(u,e_4).
% 0.52/0.69 237[4:Res:205.2,47.0] || -> product(e_4,e_3,e_1) product(e_3,e_3,e_1)* equalish(e_3,e_1).
% 0.52/0.69 248[4:MRR:237.2,13.0] || -> product(e_4,e_3,e_1) product(e_3,e_3,e_1)*.
% 0.52/0.69 249[4:Res:248.1,47.0] || -> product(e_4,e_3,e_1)* equalish(e_1,e_3).
% 0.52/0.69 260[4:MRR:249.1,8.0] || -> product(e_4,e_3,e_1)*.
% 0.52/0.69 266[4:Res:260.0,21.0] || product(e_4,u,e_1)*+ -> equalish(u,e_3).
% 0.52/0.69 310[5:Spt:220.0,220.2] || product(e_4,e_2,u)*+ -> equalish(u,e_3).
% 0.52/0.69 339[6:Spt:222.0,222.2] || product(u,e_2,e_3)*+ -> equalish(u,e_4).
% 0.52/0.69 340[6:Res:1.5,339.0] 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).
% 0.52/0.69 343[6:SSi:340.1,340.0,4.0,5.0] || -> 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).
% 0.52/0.69 344[6:MRR:343.3,9.0] || -> product(e_4,e_2,e_3) product(e_3,e_2,e_3) product(e_2,e_2,e_3)*.
% 0.52/0.69 345[6:Res:344.2,47.0] || -> product(e_4,e_2,e_3) product(e_3,e_2,e_3)* equalish(e_3,e_2).
% 0.52/0.69 356[6:MRR:345.2,14.0] || -> product(e_4,e_2,e_3) product(e_3,e_2,e_3)*.
% 0.52/0.69 358[7:Spt:356.0] || -> product(e_4,e_2,e_3)*.
% 0.52/0.69 359[7:Res:358.0,24.0] || product(u,e_3,e_4)*+ -> product(e_2,e_4,u)*.
% 0.52/0.69 361[7:Res:358.0,26.0] || product(e_2,e_4,u)*+ -> product(u,e_3,e_4)*.
% 0.52/0.69 389[7:Res:67.3,361.0] group_element(e_4) || -> product(e_4,e_4,e_1) product(e_3,e_4,e_1) equalish(e_4,e_1) product(e_1,e_3,e_4)*.
% 0.52/0.69 391[7:SSi:389.0,6.0] || -> product(e_4,e_4,e_1) product(e_3,e_4,e_1) equalish(e_4,e_1) product(e_1,e_3,e_4)*.
% 0.52/0.69 392[7:MRR:391.2,16.0] || -> product(e_4,e_4,e_1) product(e_3,e_4,e_1) product(e_1,e_3,e_4)*.
% 0.52/0.69 394[8:Spt:392.0] || -> product(e_4,e_4,e_1)*.
% 0.52/0.69 406[8:Res:394.0,266.0] || -> equalish(e_4,e_3)*.
% 0.52/0.69 408[8:MRR:406.0,18.0] || -> .
% 0.52/0.69 409[8:Spt:408.0,392.0,394.0] || product(e_4,e_4,e_1)*+ -> .
% 0.52/0.69 410[8:Spt:408.0,392.1,392.2] || -> product(e_3,e_4,e_1) product(e_1,e_3,e_4)*.
% 0.52/0.69 411[9:Spt:410.0] || -> product(e_3,e_4,e_1)*.
% 0.52/0.69 421[9:Res:411.0,122.0] || -> equalish(e_4,e_2)*.
% 0.52/0.69 422[9:MRR:421.0,17.0] || -> .
% 0.52/0.69 423[9:Spt:422.0,410.0,411.0] || product(e_3,e_4,e_1)*+ -> .
% 0.52/0.69 424[9:Spt:422.0,410.1] || -> product(e_1,e_3,e_4)*.
% 0.52/0.69 427[9:Res:424.0,24.0] || product(u,e_4,e_1)*+ -> product(e_3,e_1,u)*.
% 0.52/0.69 433[9:Res:424.0,359.0] || -> product(e_2,e_4,e_1)*.
% 0.52/0.69 451[9:Res:19.5,423.0] group_element(e_4) group_element(e_3) || -> product(e_3,e_4,e_4) product(e_3,e_4,e_3) product(e_3,e_4,e_2)*.
% 0.52/0.69 452[9:SSi:451.1,451.0,5.0,6.0] || -> product(e_3,e_4,e_4) product(e_3,e_4,e_3) product(e_3,e_4,e_2)*.
% 0.52/0.69 489[9:Res:433.0,427.0] || -> product(e_3,e_1,e_2)*.
% 0.52/0.69 506[9:Res:489.0,21.0] || product(e_3,u,e_2)*+ -> equalish(u,e_1).
% 0.52/0.69 520[9:Res:452.2,506.0] || -> product(e_3,e_4,e_4) product(e_3,e_4,e_3)* equalish(e_4,e_1).
% 0.52/0.70 522[9:MRR:520.2,16.0] || -> product(e_3,e_4,e_4) product(e_3,e_4,e_3)*.
% 0.52/0.70 523[9:Res:522.1,43.0] || -> product(e_3,e_4,e_4)* equalish(e_4,e_3).
% 0.52/0.70 535[9:MRR:523.1,18.0] || -> product(e_3,e_4,e_4)*.
% 0.52/0.70 556[9:Res:535.0,39.0] || -> equalish(e_3,e_4)*.
% 0.52/0.70 567[9:MRR:556.0,15.0] || -> .
% 0.52/0.70 569[7:Spt:567.0,356.0,358.0] || product(e_4,e_2,e_3)* -> .
% 0.52/0.70 570[7:Spt:567.0,356.1] || -> product(e_3,e_2,e_3)*.
% 0.52/0.70 584[7:Res:570.0,120.0] || -> equalish(e_3,e_1)*.
% 0.52/0.70 588[7:MRR:584.0,13.0] || -> .
% 0.52/0.70 594[6:Spt:588.0,222.1] || -> product(e_4,e_2,e_4)*.
% 0.52/0.70 606[6:Res:594.0,310.0] || -> equalish(e_4,e_3)*.
% 0.52/0.70 608[6:MRR:606.0,18.0] || -> .
% 0.52/0.70 610[5:Spt:608.0,220.1] || -> product(e_4,e_2,e_4)*.
% 0.52/0.70 611[5:Res:610.0,43.0] || -> equalish(e_2,e_4)*.
% 0.52/0.70 622[5:MRR:611.0,12.0] || -> .
% 0.52/0.70 624[3:Spt:622.0,119.1] || -> product(e_4,e_2,e_1)*.
% 0.52/0.70 630[3:Res:624.0,22.0] || product(u,e_2,e_1)*+ -> equalish(u,e_4).
% 0.52/0.70 673[4:Spt:126.0] || -> product(e_3,e_4,e_1)*.
% 0.52/0.70 682[4:Res:673.0,122.0] || -> equalish(e_4,e_2)*.
% 0.52/0.70 685[4:MRR:682.0,17.0] || -> .
% 0.52/0.70 688[4:Spt:685.0,126.0,673.0] || product(e_3,e_4,e_1)* -> .
% 0.52/0.70 689[4:Spt:685.0,126.1,126.2] || -> product(e_3,e_3,e_1) product(e_3,e_2,e_1)*.
% 0.52/0.70 695[5:Spt:689.0] || -> product(e_3,e_3,e_1)*.
% 0.52/0.70 707[5:Res:695.0,122.0] || -> equalish(e_3,e_2)*.
% 0.52/0.70 711[5:MRR:707.0,14.0] || -> .
% 0.52/0.70 714[5:Spt:711.0,689.0,695.0] || product(e_3,e_3,e_1)* -> .
% 0.52/0.70 715[5:Spt:711.0,689.1] || -> product(e_3,e_2,e_1)*.
% 0.52/0.70 731[5:Res:715.0,630.0] || -> equalish(e_3,e_4)*.
% 0.52/0.70 733[5:MRR:731.0,15.0] || -> .
% 0.52/0.70 736[2:Spt:733.0,118.1] || -> product(e_4,e_2,e_1)*.
% 0.52/0.70 737[2:Res:736.0,24.0] || product(u,e_1,e_4)*+ -> product(e_2,e_4,u)*.
% 0.52/0.70 739[2:Res:736.0,26.0] || product(e_2,e_4,u)*+ -> product(u,e_1,e_4)*.
% 0.52/0.70 741[2:Res:736.0,21.0] || product(e_4,u,e_1)*+ -> equalish(u,e_2).
% 0.52/0.70 774[2:Res:1.5,737.0] group_element(e_4) group_element(e_1) || -> product(e_4,e_1,e_4) product(e_3,e_1,e_4) product(e_2,e_1,e_4)* product(e_2,e_4,e_1).
% 0.52/0.70 775[2:SSi:774.1,774.0,3.0,6.0] || -> product(e_4,e_1,e_4) product(e_3,e_1,e_4) product(e_2,e_1,e_4)* product(e_2,e_4,e_1).
% 0.52/0.70 791[2:Res:67.3,739.0] group_element(e_4) || -> product(e_4,e_4,e_1) product(e_3,e_4,e_1) equalish(e_4,e_1) product(e_1,e_1,e_4)*.
% 0.52/0.70 793[2:SSi:791.0,6.0] || -> product(e_4,e_4,e_1) product(e_3,e_4,e_1) equalish(e_4,e_1) product(e_1,e_1,e_4)*.
% 0.52/0.70 794[2:MRR:793.2,16.0] || -> product(e_4,e_4,e_1) product(e_3,e_4,e_1) product(e_1,e_1,e_4)*.
% 0.52/0.70 796[2:Res:794.2,47.0] || -> product(e_4,e_4,e_1) product(e_3,e_4,e_1)* equalish(e_4,e_1).
% 0.52/0.70 814[2:MRR:796.2,16.0] || -> product(e_4,e_4,e_1) product(e_3,e_4,e_1)*.
% 0.52/0.70 820[2:Res:814.1,21.0] || product(e_3,u,e_1)*+ -> product(e_4,e_4,e_1) equalish(u,e_4).
% 0.52/0.70 848[3:Spt:820.0,820.2] || product(e_3,u,e_1)*+ -> equalish(u,e_4).
% 0.52/0.70 849[3:Res:2.5,848.0] 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_4).
% 0.52/0.70 853[3:SSi:849.1,849.0,5.0,3.0] || -> 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_4).
% 0.52/0.70 854[3:MRR:853.3,9.0] || -> product(e_3,e_4,e_1) product(e_3,e_3,e_1) product(e_3,e_2,e_1)*.
% 0.52/0.70 865[3:Res:854.2,848.0] || -> product(e_3,e_4,e_1) product(e_3,e_3,e_1)* equalish(e_2,e_4).
% 0.52/0.70 870[3:MRR:865.2,12.0] || -> product(e_3,e_4,e_1) product(e_3,e_3,e_1)*.
% 0.52/0.70 872[3:Res:870.1,47.0] || -> product(e_3,e_4,e_1)* equalish(e_1,e_3).
% 0.52/0.70 888[3:MRR:872.1,8.0] || -> product(e_3,e_4,e_1)*.
% 0.52/0.70 904[3:Res:888.0,24.0] || product(u,e_1,e_3)*+ -> product(e_4,e_3,u)*.
% 0.52/0.70 929[3:Res:1.5,904.0] group_element(e_3) group_element(e_1) || -> product(e_4,e_1,e_3) product(e_3,e_1,e_3) product(e_2,e_1,e_3)* product(e_4,e_3,e_1).
% 0.52/0.70 930[3:SSi:929.1,929.0,3.0,5.0] || -> product(e_4,e_1,e_3) product(e_3,e_1,e_3) product(e_2,e_1,e_3)* product(e_4,e_3,e_1).
% 0.52/0.70 955[4:Spt:775.0] || -> product(e_4,e_1,e_4)*.
% 0.52/0.70 956[4:Res:955.0,43.0] || -> equalish(e_1,e_4)*.
% 0.52/0.70 973[4:MRR:956.0,9.0] || -> .
% 0.52/0.70 979[4:Spt:973.0,775.0,955.0] || product(e_4,e_1,e_4)*+ -> .
% 0.52/0.70 980[4:Spt:973.0,775.1,775.2,775.3] || -> product(e_3,e_1,e_4) product(e_2,e_1,e_4)* product(e_2,e_4,e_1).
% 0.52/0.70 982[5:Spt:980.0] || -> product(e_3,e_1,e_4)*.
% 0.52/0.70 986[5:Res:982.0,20.0] || product(e_3,e_1,u)*+ -> equalish(u,e_4).
% 0.52/0.70 989[5:Res:982.0,737.0] || -> product(e_2,e_4,e_3)*.
% 0.52/0.70 1004[5:Res:989.0,21.0] || product(e_2,u,e_3)*+ -> equalish(u,e_4).
% 0.52/0.70 1156[6:Spt:930.0] || -> product(e_4,e_1,e_3)*.
% 0.52/0.70 1164[6:Res:1156.0,904.0] || -> product(e_4,e_3,e_4)*.
% 0.52/0.70 1193[2:Res:69.3,737.0] group_element(e_4) || -> product(e_4,e_1,e_4) product(e_3,e_1,e_4) equalish(e_4,e_1) product(e_2,e_4,e_2)*.
% 0.52/0.70 1209[5:Res:69.3,1004.0] group_element(e_3) || -> product(e_4,e_1,e_3) product(e_3,e_1,e_3)* equalish(e_3,e_1) equalish(e_1,e_4).
% 0.52/0.70 1228[6:Res:1164.0,43.0] || -> equalish(e_3,e_4)*.
% 0.52/0.70 1244[6:MRR:1228.0,15.0] || -> .
% 0.52/0.70 1247[6:Spt:1244.0,930.0,1156.0] || product(e_4,e_1,e_3)* -> .
% 0.52/0.70 1248[6:Spt:1244.0,930.1,930.2,930.3] || -> product(e_3,e_1,e_3) product(e_2,e_1,e_3)* product(e_4,e_3,e_1).
% 0.52/0.70 1250[5:SSi:1209.0,5.0] || -> product(e_4,e_1,e_3) product(e_3,e_1,e_3)* equalish(e_3,e_1) equalish(e_1,e_4).
% 0.52/0.70 1251[5:MRR:1250.2,1250.3,13.0,9.0] || -> product(e_4,e_1,e_3) product(e_3,e_1,e_3)*.
% 0.52/0.70 1252[6:MRR:1251.0,1247.0] || -> product(e_3,e_1,e_3)*.
% 0.52/0.70 1274[6:Res:1252.0,986.0] || -> equalish(e_3,e_4)*.
% 0.52/0.70 1276[6:MRR:1274.0,15.0] || -> .
% 0.52/0.70 1284[5:Spt:1276.0,980.0,982.0] || product(e_3,e_1,e_4)* -> .
% 0.52/0.70 1285[5:Spt:1276.0,980.1,980.2] || -> product(e_2,e_1,e_4)* product(e_2,e_4,e_1).
% 0.52/0.70 1289[2:SSi:1193.0,6.0] || -> product(e_4,e_1,e_4) product(e_3,e_1,e_4) equalish(e_4,e_1) product(e_2,e_4,e_2)*.
% 0.52/0.70 1290[4:MRR:1289.0,1289.2,979.0,16.0] || -> product(e_3,e_1,e_4) product(e_2,e_4,e_2)*.
% 0.52/0.70 1291[5:MRR:1290.0,1284.0] || -> product(e_2,e_4,e_2)*.
% 0.52/0.70 1315[5:Res:1291.0,43.0] || -> equalish(e_4,e_2)*.
% 0.52/0.70 1331[5:MRR:1315.0,17.0] || -> .
% 0.52/0.70 1334[3:Spt:1331.0,820.1] || -> product(e_4,e_4,e_1)*.
% 0.52/0.70 1352[3:Res:1334.0,741.0] || -> equalish(e_4,e_2)*.
% 0.52/0.70 1358[3:MRR:1352.0,17.0] || -> .
% 0.52/0.70 1365[1:Spt:1358.0,117.1] || -> product(e_4,e_2,e_1)*.
% 0.52/0.70 1367[1:Res:1365.0,24.0] || product(u,e_1,e_4)*+ -> product(e_2,e_4,u)*.
% 0.52/0.70 1368[1:Res:1365.0,25.0] || product(e_1,u,e_2)*+ -> product(e_2,e_4,u).
% 0.52/0.70 1494[0:Res:93.3,39.0] group_element(e_2) || -> product(e_1,e_4,e_2) product(e_1,e_3,e_2)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.52/0.70 1520[0:SSi:1494.0,4.0] || -> product(e_1,e_4,e_2) product(e_1,e_3,e_2)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.52/0.70 1521[0:MRR:1520.2,1520.3,10.0,7.0] || -> product(e_1,e_4,e_2) product(e_1,e_3,e_2)*.
% 0.52/0.70 1570[1:Res:1521.1,1368.0] || -> product(e_1,e_4,e_2)* product(e_2,e_4,e_3).
% 0.52/0.70 1572[2:Spt:1570.0] || -> product(e_1,e_4,e_2)*.
% 0.52/0.70 1589[2:Res:1572.0,1368.0] || -> product(e_2,e_4,e_4)*.
% 0.52/0.70 1637[2:Res:1589.0,39.0] || -> equalish(e_2,e_4)*.
% 0.52/0.70 1651[2:MRR:1637.0,12.0] || -> .
% 0.52/0.70 1654[2:Spt:1651.0,1570.0,1572.0] || product(e_1,e_4,e_2)*+ -> .
% 0.52/0.70 1655[2:Spt:1651.0,1570.1] || -> product(e_2,e_4,e_3)*.
% 0.52/0.70 1674[2:Res:1655.0,21.0] || product(e_2,u,e_3)*+ -> equalish(u,e_4).
% 0.52/0.70 1804[0:Res:146.3,43.0] 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).
% 0.52/0.70 1829[0:SSi:1804.0,4.0] || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.52/0.70 1830[0:MRR:1829.2,1829.3,10.0,7.0] || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)*.
% 0.52/0.70 1844[3:Spt:1830.0] || -> product(e_2,e_1,e_4)*.
% 0.52/0.70 1853[3:Res:1844.0,1367.0] || -> product(e_2,e_4,e_2)*.
% 0.52/0.70 1867[3:Res:1853.0,43.0] || -> equalish(e_4,e_2)*.
% 0.52/0.70 1882[3:MRR:1867.0,17.0] || -> .
% 0.52/0.70 1885[3:Spt:1882.0,1830.0,1844.0] || product(e_2,e_1,e_4)*+ -> .
% 0.52/0.70 1886[3:Spt:1882.0,1830.1] || -> product(e_2,e_1,e_3)*.
% 0.52/0.70 2104[3:Res:1886.0,1674.0] || -> equalish(e_1,e_4)*.
% 0.52/0.70 2105[3:MRR:2104.0,9.0] || -> .
% 0.52/0.70 % SZS output end Refutation
% 0.52/0.70 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 qg4_1 qg4_2 qg4
% 0.52/0.70
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