TSTP Solution File: GRP130-3.003 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP130-3.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:45:47 EDT 2022
% Result : Unsatisfiable 0.41s 0.60s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP130-3.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 18:09:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.60
% 0.41/0.60 SPASS V 3.9
% 0.41/0.60 SPASS beiseite: Proof found.
% 0.41/0.60 % SZS status Theorem
% 0.41/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.60 SPASS derived 1148 clauses, backtracked 517 clauses, performed 31 splits and kept 1141 clauses.
% 0.41/0.60 SPASS allocated 76687 KBytes.
% 0.41/0.60 SPASS spent 0:00:00.26 on the problem.
% 0.41/0.60 0:00:00.03 for the input.
% 0.41/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.41/0.60 0:00:00.02 for inferences.
% 0.41/0.60 0:00:00.00 for the backtracking.
% 0.41/0.60 0:00:00.18 for the reduction.
% 0.41/0.60
% 0.41/0.60
% 0.41/0.60 Here is a proof with depth 17, length 324 :
% 0.41/0.60 % SZS output start Refutation
% 0.41/0.60 1[0:Inp] || -> next(e_0,e_1)*.
% 0.41/0.60 2[0:Inp] || -> next(e_1,e_2)*.
% 0.41/0.60 3[0:Inp] || -> next(e_2,e_3)*.
% 0.41/0.60 4[0:Inp] || -> greater(e_1,e_0)*.
% 0.41/0.60 5[0:Inp] || -> greater(e_2,e_0)*.
% 0.41/0.60 7[0:Inp] || -> greater(e_2,e_1)*.
% 0.41/0.60 8[0:Inp] || -> greater(e_3,e_1)*.
% 0.41/0.60 9[0:Inp] || -> greater(e_3,e_2)*.
% 0.41/0.60 11[0:Inp] group_element(u) || -> cycle(u,e_2) cycle(u,e_1) cycle(u,e_0)*.
% 0.41/0.60 12[0:Inp] || -> cycle(e_3,e_0)*.
% 0.41/0.60 13[0:Inp] || next(u,v)*+ next(w,x)* cycle(x,u)* cycle(w,y)* greater(y,e_0) -> equalish(y,v)*.
% 0.41/0.60 14[0:Inp] || greater(u,v)*+ greater(w,x)* next(w,y)* cycle(y,v)* cycle(x,u)* cycle(w,e_0) -> .
% 0.41/0.60 15[0:Inp] || greater(u,v) cycle(v,e_0) product(v,e_1,u)*+ -> .
% 0.41/0.60 16[0:Inp] || next(u,v)* cycle(u,w)* greater(w,e_0)* product(u,e_1,x)*+ -> equalish(x,v)*.
% 0.41/0.60 17[0:Inp] || -> group_element(e_1)*.
% 0.41/0.60 18[0:Inp] || -> group_element(e_2)*.
% 0.41/0.60 19[0:Inp] || -> group_element(e_3)*.
% 0.41/0.60 20[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.41/0.60 21[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.41/0.60 22[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.41/0.60 23[0:Inp] || equalish(e_2,e_3)*+ -> .
% 0.41/0.60 24[0:Inp] || equalish(e_3,e_1)*+ -> .
% 0.41/0.60 25[0:Inp] || equalish(e_3,e_2)*+ -> .
% 0.41/0.60 26[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 0.41/0.60 27[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.41/0.60 28[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.41/0.60 29[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.41/0.60 30[0:Inp] || product(u,v,w)*+ product(u,x,v)* -> product(w,x,u)*.
% 0.41/0.60 42[0:Res:26.4,30.0] group_element(u) group_element(v) || product(v,w,u)*+ -> product(v,u,e_3) product(v,u,e_2)* product(e_1,w,v)*.
% 0.41/0.60 43[0:Res:26.4,27.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_3) product(v,u,e_2)* equalish(w,e_1).
% 0.41/0.60 48[0:Res:26.4,16.3] group_element(e_1) group_element(u) || next(u,v)* cycle(u,w)* greater(w,e_0)* -> product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_1,v)*.
% 0.41/0.60 49[0:SSi:48.0,17.0] group_element(u) || next(u,v)*+ cycle(u,w)* greater(w,e_0)* -> product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_1,v)*.
% 0.41/0.60 55[0:Res:2.0,13.0] || next(u,v)*+ cycle(v,e_1) cycle(u,w)* greater(w,e_0) -> equalish(w,e_2)*.
% 0.41/0.60 56[0:Res:1.0,13.0] || next(u,v)*+ cycle(v,e_0) cycle(u,w)* greater(w,e_0) -> equalish(w,e_1)*.
% 0.41/0.60 64[0:Res:5.0,14.0] || greater(u,v)*+ next(u,w)* cycle(w,e_0) cycle(v,e_2) cycle(u,e_0) -> .
% 0.41/0.60 65[0:Res:4.0,14.0] || greater(u,v)*+ next(u,w)* cycle(w,e_0) cycle(v,e_1) cycle(u,e_0) -> .
% 0.41/0.60 67[0:Res:2.0,55.0] || cycle(e_2,e_1)+ cycle(e_1,u) greater(u,e_0) -> equalish(u,e_2)*.
% 0.41/0.60 69[0:Res:3.0,56.0] || cycle(e_3,e_0) cycle(e_2,u) greater(u,e_0) -> equalish(u,e_1)*.
% 0.41/0.60 70[0:Res:2.0,56.0] || cycle(e_2,e_0)+ cycle(e_1,u) greater(u,e_0) -> equalish(u,e_1)*.
% 0.41/0.60 72[0:MRR:69.0,12.0] || cycle(e_2,u)+ greater(u,e_0) -> equalish(u,e_1)*.
% 0.41/0.60 73[0:Res:11.3,72.0] group_element(e_2) || greater(e_0,e_0) -> cycle(e_2,e_2) cycle(e_2,e_1) equalish(e_0,e_1)*.
% 0.41/0.60 74[0:SSi:73.0,18.0] || greater(e_0,e_0)+ -> cycle(e_2,e_2) cycle(e_2,e_1) equalish(e_0,e_1)*.
% 0.41/0.60 75[0:Res:11.3,70.0] group_element(e_2) || cycle(e_1,u) greater(u,e_0) -> cycle(e_2,e_2) cycle(e_2,e_1) equalish(u,e_1)*.
% 0.41/0.60 76[0:SSi:75.0,18.0] || cycle(e_1,u) greater(u,e_0) -> cycle(e_2,e_2) cycle(e_2,e_1) equalish(u,e_1)*.
% 0.41/0.60 82[0:Res:7.0,65.0] || next(e_2,u)*+ cycle(u,e_0) cycle(e_1,e_1) cycle(e_2,e_0) -> .
% 0.41/0.60 88[0:Res:3.0,82.0] || cycle(e_3,e_0) cycle(e_1,e_1)* cycle(e_2,e_0) -> .
% 0.41/0.60 89[0:MRR:88.0,12.0] || cycle(e_1,e_1)*+ cycle(e_2,e_0) -> .
% 0.41/0.60 93[0:Res:7.0,64.0] || next(e_2,u)*+ cycle(u,e_0) cycle(e_1,e_2) cycle(e_2,e_0) -> .
% 0.41/0.60 138[0:Res:3.0,93.0] || cycle(e_3,e_0) cycle(e_1,e_2)* cycle(e_2,e_0) -> .
% 0.41/0.60 139[0:MRR:138.0,12.0] || cycle(e_1,e_2)*+ cycle(e_2,e_0) -> .
% 0.41/0.60 140[0:Res:26.4,43.2] group_element(u) group_element(v) group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* product(v,u,e_3) product(v,u,e_2)* equalish(e_1,e_1).
% 0.41/0.60 141[0:Obv:140.5] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* equalish(e_1,e_1).
% 0.41/0.60 145[0:Res:26.4,42.2] group_element(u) group_element(v) group_element(e_1) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* product(v,e_1,e_3) product(v,e_1,e_2)* product(e_1,u,v)*.
% 0.41/0.60 146[0:Obv:145.1] group_element(u) group_element(e_1) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* product(v,e_1,e_3) product(v,e_1,e_2)* product(e_1,u,v)*.
% 0.41/0.60 147[0:SSi:146.1,17.0] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* product(v,e_1,e_3) product(v,e_1,e_2)* product(e_1,u,v)*.
% 0.41/0.60 151[0:Res:3.0,49.1] group_element(e_2) || cycle(e_2,u) greater(u,e_0)* -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)* equalish(e_1,e_3).
% 0.41/0.60 152[0:Res:2.0,49.1] group_element(e_1) || cycle(e_1,u) greater(u,e_0)* -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 0.41/0.60 154[0:SSi:152.0,17.0] || cycle(e_1,u) greater(u,e_0)* -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)* equalish(e_1,e_2).
% 0.41/0.60 155[0:MRR:154.4,20.0] || cycle(e_1,u)+ greater(u,e_0)* -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 0.41/0.60 156[0:SSi:151.0,18.0] || cycle(e_2,u) greater(u,e_0)* -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)* equalish(e_1,e_3).
% 0.41/0.60 157[0:MRR:156.4,21.0] || cycle(e_2,u)+ greater(u,e_0)* -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.41/0.60 163[0:Res:11.3,155.0] group_element(e_1) || greater(e_0,e_0) -> cycle(e_1,e_2) cycle(e_1,e_1) product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 0.41/0.60 164[0:SSi:163.0,17.0] || greater(e_0,e_0) -> cycle(e_1,e_2) cycle(e_1,e_1) product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 0.41/0.60 165[0:Res:11.3,157.0] group_element(e_2) || greater(e_0,e_0) -> cycle(e_2,e_2) cycle(e_2,e_1) product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.41/0.60 166[0:SSi:165.0,18.0] || greater(e_0,e_0) -> cycle(e_2,e_2) cycle(e_2,e_1) product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.41/0.60 167[1:Spt:141.0,141.1,141.2,141.3] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)*.
% 0.41/0.60 168[1:Res:167.3,15.2] group_element(e_1) group_element(u) || greater(e_2,u) cycle(u,e_0) -> product(u,e_1,e_3)*.
% 0.41/0.60 169[1:Res:167.3,30.0] group_element(u) group_element(v) || product(v,w,u)*+ -> product(v,u,e_3)* product(e_2,w,v)*.
% 0.41/0.60 170[1:Res:167.3,27.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_3)* equalish(w,e_2).
% 0.41/0.60 174[1:SSi:168.0,17.0] group_element(u) || greater(e_2,u)+ cycle(u,e_0) -> product(u,e_1,e_3)*.
% 0.41/0.60 176[1:Res:7.0,174.1] group_element(e_1) || cycle(e_1,e_0) -> product(e_1,e_1,e_3)*.
% 0.41/0.60 178[1:SSi:176.0,17.0] || cycle(e_1,e_0)+ -> product(e_1,e_1,e_3)*.
% 0.41/0.60 179[1:Res:11.3,178.0] group_element(e_1) || -> cycle(e_1,e_2) cycle(e_1,e_1) product(e_1,e_1,e_3)*.
% 0.41/0.60 180[1:SSi:179.0,17.0] || -> cycle(e_1,e_2) cycle(e_1,e_1) product(e_1,e_1,e_3)*.
% 0.41/0.60 181[2:Spt:180.0] || -> cycle(e_1,e_2)*.
% 0.41/0.60 185[2:MRR:139.0,181.0] || cycle(e_2,e_0)*+ -> .
% 0.41/0.60 188[2:Res:181.0,155.0] || greater(e_2,e_0) -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 0.41/0.60 189[2:MRR:188.0,5.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 0.41/0.60 190[2:Res:11.3,185.0] group_element(e_2) || -> cycle(e_2,e_2) cycle(e_2,e_1)*.
% 0.41/0.60 191[2:SSi:190.0,18.0] || -> cycle(e_2,e_2) cycle(e_2,e_1)*.
% 0.41/0.60 192[3:Spt:191.0] || -> cycle(e_2,e_2)*.
% 0.41/0.60 198[3:Res:192.0,72.0] || greater(e_2,e_0) -> equalish(e_2,e_1)*.
% 0.41/0.60 199[3:MRR:198.0,198.1,5.0,22.0] || -> .
% 0.41/0.60 201[3:Spt:199.0,191.0,192.0] || cycle(e_2,e_2)*+ -> .
% 0.41/0.60 202[3:Spt:199.0,191.1] || -> cycle(e_2,e_1)*.
% 0.41/0.60 215[2:Res:189.1,27.0] || product(e_1,e_1,u)*+ -> product(e_1,e_1,e_3)* equalish(u,e_2).
% 0.41/0.60 217[2:Res:189.1,29.0] || product(u,e_1,e_2)*+ -> product(e_1,e_1,e_3)* equalish(u,e_1).
% 0.41/0.60 220[4:Spt:215.0,215.2] || product(e_1,e_1,u)*+ -> equalish(u,e_2).
% 0.41/0.60 235[5:Spt:217.0,217.2] || product(u,e_1,e_2)*+ -> equalish(u,e_1).
% 0.41/0.60 237[5:Res:167.3,235.0] group_element(e_1) group_element(u) || -> product(u,e_1,e_3)* equalish(u,e_1).
% 0.41/0.60 238[5:SSi:237.0,17.0] group_element(u) || -> product(u,e_1,e_3)* equalish(u,e_1).
% 0.41/0.60 292[3:Res:202.0,157.0] || greater(e_1,e_0) -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.41/0.60 293[3:MRR:292.0,4.0] || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.41/0.60 299[5:Res:293.1,235.0] || -> product(e_2,e_1,e_3)* equalish(e_2,e_1).
% 0.41/0.60 301[5:MRR:299.1,22.0] || -> product(e_2,e_1,e_3)*.
% 0.41/0.60 306[5:Res:301.0,29.0] || product(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.41/0.60 322[5:Res:238.1,306.0] group_element(u) || -> equalish(u,e_1)* equalish(u,e_2).
% 0.41/0.60 325[5:Res:322.1,24.0] group_element(e_3) || -> equalish(e_3,e_2)*.
% 0.41/0.60 327[5:SSi:325.0,19.0] || -> equalish(e_3,e_2)*.
% 0.41/0.60 328[5:MRR:327.0,25.0] || -> .
% 0.41/0.60 329[5:Spt:328.0,217.1] || -> product(e_1,e_1,e_3)*.
% 0.41/0.60 336[5:Res:329.0,220.0] || -> equalish(e_3,e_2)*.
% 0.41/0.60 338[5:MRR:336.0,25.0] || -> .
% 0.41/0.60 342[4:Spt:338.0,215.1] || -> product(e_1,e_1,e_3)*.
% 0.41/0.60 346[4:Res:342.0,28.0] || product(e_1,u,e_3)*+ -> equalish(u,e_1).
% 0.41/0.60 347[4:Res:342.0,29.0] || product(u,e_1,e_3)*+ -> equalish(u,e_1).
% 0.41/0.60 355[5:Spt:293.0] || -> product(e_2,e_1,e_3)*.
% 0.41/0.60 370[5:Res:355.0,347.0] || -> equalish(e_2,e_1)*.
% 0.41/0.60 371[5:MRR:370.0,22.0] || -> .
% 0.41/0.60 372[5:Spt:371.0,293.0,355.0] || product(e_2,e_1,e_3)*+ -> .
% 0.41/0.60 373[5:Spt:371.0,293.1] || -> product(e_2,e_1,e_2)*.
% 0.41/0.60 393[4:Res:342.0,169.2] group_element(e_3) group_element(e_1) || -> product(e_1,e_3,e_3)* product(e_2,e_1,e_1).
% 0.41/0.60 395[4:SSi:393.1,393.0,17.0,19.0] || -> product(e_1,e_3,e_3)* product(e_2,e_1,e_1).
% 0.41/0.60 405[4:Res:395.0,346.0] || -> product(e_2,e_1,e_1)* equalish(e_3,e_1).
% 0.41/0.60 406[4:MRR:405.1,24.0] || -> product(e_2,e_1,e_1)*.
% 0.41/0.60 413[4:Res:406.0,170.2] group_element(e_1) group_element(e_2) || -> product(e_2,e_1,e_3)* equalish(e_1,e_2).
% 0.41/0.60 417[4:SSi:413.1,413.0,18.0,17.0] || -> product(e_2,e_1,e_3)* equalish(e_1,e_2).
% 0.41/0.60 418[5:MRR:417.0,417.1,372.0,20.0] || -> .
% 0.41/0.60 419[2:Spt:418.0,180.0,181.0] || cycle(e_1,e_2)*+ -> .
% 0.41/0.60 420[2:Spt:418.0,180.1,180.2] || -> cycle(e_1,e_1) product(e_1,e_1,e_3)*.
% 0.41/0.60 422[3:Spt:420.0] || -> cycle(e_1,e_1)*.
% 0.41/0.60 424[3:MRR:89.0,422.0] || cycle(e_2,e_0)*+ -> .
% 0.41/0.60 428[3:Res:11.3,424.0] group_element(e_2) || -> cycle(e_2,e_2) cycle(e_2,e_1)*.
% 0.41/0.60 429[3:SSi:428.0,18.0] || -> cycle(e_2,e_2) cycle(e_2,e_1)*.
% 0.41/0.60 430[4:Spt:429.0] || -> cycle(e_2,e_2)*.
% 0.41/0.60 442[4:Res:430.0,72.0] || greater(e_2,e_0) -> equalish(e_2,e_1)*.
% 0.41/0.60 443[4:MRR:442.0,442.1,5.0,22.0] || -> .
% 0.41/0.60 444[4:Spt:443.0,429.0,430.0] || cycle(e_2,e_2)*+ -> .
% 0.41/0.60 445[4:Spt:443.0,429.1] || -> cycle(e_2,e_1)*.
% 0.41/0.60 447[4:MRR:67.0,445.0] || cycle(e_1,u)+ greater(u,e_0) -> equalish(u,e_2)*.
% 0.41/0.60 456[4:Res:422.0,447.0] || greater(e_1,e_0) -> equalish(e_1,e_2)*.
% 0.41/0.60 457[4:MRR:456.0,456.1,4.0,20.0] || -> .
% 0.41/0.60 458[3:Spt:457.0,420.0,422.0] || cycle(e_1,e_1)*+ -> .
% 0.41/0.60 459[3:Spt:457.0,420.1] || -> product(e_1,e_1,e_3)*.
% 0.41/0.60 461[3:Res:459.0,15.2] || greater(e_3,e_1)* cycle(e_1,e_0) -> .
% 0.41/0.60 469[3:MRR:461.0,8.0] || cycle(e_1,e_0)*+ -> .
% 0.41/0.60 472[3:Res:11.3,469.0] group_element(e_1) || -> cycle(e_1,e_2) cycle(e_1,e_1)*.
% 0.41/0.60 473[3:SSi:472.0,17.0] || -> cycle(e_1,e_2) cycle(e_1,e_1)*.
% 0.41/0.60 474[3:MRR:473.0,473.1,419.0,458.0] || -> .
% 0.41/0.60 475[1:Spt:474.0,141.4] || -> equalish(e_1,e_1)*.
% 0.41/0.60 491[2:Spt:74.1] || -> cycle(e_2,e_2)*.
% 0.41/0.60 498[2:Res:491.0,72.0] || greater(e_2,e_0) -> equalish(e_2,e_1)*.
% 0.41/0.60 499[2:MRR:498.0,498.1,5.0,22.0] || -> .
% 0.41/0.60 500[2:Spt:499.0,74.1,491.0] || cycle(e_2,e_2)*+ -> .
% 0.41/0.60 501[2:Spt:499.0,74.0,74.2,74.3] || greater(e_0,e_0)+ -> cycle(e_2,e_1) equalish(e_0,e_1)*.
% 0.41/0.60 502[2:MRR:76.2,500.0] || cycle(e_1,u) greater(u,e_0) -> cycle(e_2,e_1) equalish(u,e_1)*.
% 0.41/0.60 503[2:MRR:166.1,500.0] || greater(e_0,e_0) -> cycle(e_2,e_1) product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.41/0.60 504[3:Spt:501.1] || -> cycle(e_2,e_1)*.
% 0.41/0.60 506[3:MRR:67.0,504.0] || cycle(e_1,u)+ greater(u,e_0) -> equalish(u,e_2)*.
% 0.41/0.60 514[3:Res:11.3,506.0] group_element(e_1) || greater(e_0,e_0) -> cycle(e_1,e_2) cycle(e_1,e_1) equalish(e_0,e_2)*.
% 0.41/0.60 515[3:SSi:514.0,17.0] || greater(e_0,e_0)+ -> cycle(e_1,e_2) cycle(e_1,e_1) equalish(e_0,e_2)*.
% 0.41/0.60 517[4:Spt:515.1] || -> cycle(e_1,e_2)*.
% 0.41/0.60 531[3:Res:504.0,157.0] || greater(e_1,e_0) -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.41/0.60 532[3:MRR:531.0,4.0] || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.41/0.60 534[3:Res:532.1,30.0] || product(e_2,u,e_1)*+ -> product(e_2,e_1,e_3)* product(e_2,u,e_2).
% 0.41/0.60 535[3:Res:532.1,27.0] || product(e_2,e_1,u)*+ -> product(e_2,e_1,e_3)* equalish(u,e_2).
% 0.41/0.60 536[3:Res:532.1,28.0] || product(e_2,u,e_2)*+ -> product(e_2,e_1,e_3)* equalish(u,e_1).
% 0.41/0.60 537[3:Res:532.1,29.0] || product(u,e_1,e_2)*+ -> product(e_2,e_1,e_3)* equalish(u,e_2).
% 0.41/0.60 540[3:Res:532.1,42.2] group_element(e_2) group_element(e_2) || -> product(e_2,e_1,e_3) product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_1,e_1,e_2)*.
% 0.41/0.60 542[3:Obv:540.0] group_element(e_2) || -> product(e_2,e_1,e_3) product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_1,e_1,e_2)*.
% 0.41/0.60 543[3:SSi:542.0,18.0] || -> product(e_2,e_1,e_3) product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_1,e_1,e_2)*.
% 0.41/0.60 544[5:Spt:535.0,535.2] || product(e_2,e_1,u)*+ -> equalish(u,e_2).
% 0.41/0.60 549[6:Spt:537.0,537.2] || product(u,e_1,e_2)*+ -> equalish(u,e_2).
% 0.41/0.60 552[4:Res:517.0,155.0] || greater(e_2,e_0) -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 0.41/0.60 553[4:MRR:552.0,5.0] || -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 0.41/0.60 558[4:Res:553.1,29.0] || product(u,e_1,e_2)* -> product(e_1,e_1,e_3)* equalish(u,e_1).
% 0.41/0.60 559[6:Res:553.1,549.0] || -> product(e_1,e_1,e_3)* equalish(e_1,e_2).
% 0.41/0.60 563[6:MRR:559.1,20.0] || -> product(e_1,e_1,e_3)*.
% 0.41/0.60 567[6:Res:563.0,27.0] || product(e_1,e_1,u)*+ -> equalish(u,e_3).
% 0.41/0.60 568[6:Res:563.0,28.0] || product(e_1,u,e_3)*+ -> equalish(u,e_1).
% 0.41/0.60 572[6:Res:563.0,42.2] group_element(e_3) group_element(e_1) || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2) product(e_1,e_1,e_1)*.
% 0.41/0.60 575[6:SSi:572.1,572.0,17.0,19.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2) product(e_1,e_1,e_1)*.
% 0.41/0.60 580[0:Fac:147.3,147.5] group_element(e_1) group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_3) product(u,e_1,e_2)* product(e_1,e_1,u)*.
% 0.41/0.60 609[0:Obv:580.2] group_element(e_1) group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* product(e_1,e_1,u)*.
% 0.41/0.60 610[0:SSi:609.0,17.0] group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* product(e_1,e_1,u)*.
% 0.41/0.60 689[6:Res:575.2,567.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)* equalish(e_1,e_3).
% 0.41/0.60 691[6:MRR:689.2,21.0] || -> product(e_1,e_3,e_3) product(e_1,e_3,e_2)*.
% 0.41/0.60 695[6:Res:691.1,27.0] || product(e_1,e_3,u)*+ -> product(e_1,e_3,e_3)* equalish(u,e_2).
% 0.41/0.60 697[6:Res:691.1,29.0] || product(u,e_3,e_2)*+ -> product(e_1,e_3,e_3)* equalish(u,e_1).
% 0.41/0.60 702[7:Spt:695.0,695.2] || product(e_1,e_3,u)*+ -> equalish(u,e_2).
% 0.41/0.60 766[8:Spt:697.0,697.2] || product(u,e_3,e_2)*+ -> equalish(u,e_1).
% 0.41/0.60 777[9:Spt:534.0,534.2] || product(e_2,u,e_1)*+ -> product(e_2,u,e_2).
% 0.41/0.60 778[9:Res:26.4,777.0] group_element(u) group_element(e_2) || -> product(e_2,u,e_3) product(e_2,u,e_2)* product(e_2,u,e_2)*.
% 0.41/0.60 779[9:Obv:778.3] group_element(u) group_element(e_2) || -> product(e_2,u,e_3) product(e_2,u,e_2)*.
% 0.41/0.60 780[9:SSi:779.1,18.0] group_element(u) || -> product(e_2,u,e_3) product(e_2,u,e_2)*.
% 0.41/0.60 788[9:Res:780.2,766.0] group_element(e_3) || -> product(e_2,e_3,e_3)* equalish(e_2,e_1).
% 0.41/0.60 793[9:SSi:788.0,19.0] || -> product(e_2,e_3,e_3)* equalish(e_2,e_1).
% 0.41/0.60 794[9:MRR:793.1,22.0] || -> product(e_2,e_3,e_3)*.
% 0.41/0.60 797[9:Res:794.0,30.0] || product(e_2,u,e_3)*+ -> product(e_3,u,e_2).
% 0.41/0.60 850[9:Res:794.0,797.0] || -> product(e_3,e_3,e_2)*.
% 0.41/0.60 876[9:Res:850.0,766.0] || -> equalish(e_3,e_1)*.
% 0.41/0.60 879[9:MRR:876.0,24.0] || -> .
% 0.41/0.60 882[9:Spt:879.0,534.1] || -> product(e_2,e_1,e_3)*.
% 0.41/0.60 893[9:Res:882.0,544.0] || -> equalish(e_3,e_2)*.
% 0.41/0.60 895[9:MRR:893.0,25.0] || -> .
% 0.41/0.60 909[8:Spt:895.0,697.1] || -> product(e_1,e_3,e_3)*.
% 0.41/0.60 917[8:Res:909.0,702.0] || -> equalish(e_3,e_2)*.
% 0.41/0.60 919[8:MRR:917.0,25.0] || -> .
% 0.41/0.60 926[7:Spt:919.0,695.1] || -> product(e_1,e_3,e_3)*.
% 0.41/0.60 933[7:Res:926.0,568.0] || -> equalish(e_3,e_1)*.
% 0.41/0.60 934[7:MRR:933.0,24.0] || -> .
% 0.41/0.60 936[6:Spt:934.0,537.1] || -> product(e_2,e_1,e_3)*.
% 0.41/0.60 946[6:Res:936.0,544.0] || -> equalish(e_3,e_2)*.
% 0.41/0.60 947[6:MRR:946.0,25.0] || -> .
% 0.41/0.60 954[5:Spt:947.0,535.1] || -> product(e_2,e_1,e_3)*.
% 0.41/0.60 959[5:Res:954.0,29.0] || product(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.41/0.60 964[6:Spt:553.0] || -> product(e_1,e_1,e_3)*.
% 0.41/0.60 999[5:Res:610.3,959.0] group_element(e_3) || -> product(e_3,e_1,e_3) product(e_3,e_1,e_2)* equalish(e_1,e_2).
% 0.41/0.60 1000[6:Res:964.0,959.0] || -> equalish(e_1,e_2)*.
% 0.41/0.60 1002[6:MRR:1000.0,20.0] || -> .
% 0.41/0.60 1003[5:SSi:999.0,19.0] || -> product(e_3,e_1,e_3) product(e_3,e_1,e_2)* equalish(e_1,e_2).
% 0.41/0.60 1004[5:MRR:1003.2,20.0] || -> product(e_3,e_1,e_3) product(e_3,e_1,e_2)*.
% 0.41/0.61 1006[6:Spt:1002.0,553.0,964.0] || product(e_1,e_1,e_3)*+ -> .
% 0.41/0.61 1007[6:Spt:1002.0,553.1] || -> product(e_1,e_1,e_2)*.
% 0.41/0.61 1011[6:MRR:558.1,1006.0] || product(u,e_1,e_2)*+ -> equalish(u,e_1).
% 0.41/0.61 1085[6:Res:1004.1,1011.0] || -> product(e_3,e_1,e_3)* equalish(e_3,e_1).
% 0.41/0.61 1086[6:MRR:1085.1,24.0] || -> product(e_3,e_1,e_3)*.
% 0.41/0.61 1098[6:Res:1086.0,959.0] || -> equalish(e_3,e_2)*.
% 0.41/0.61 1102[6:MRR:1098.0,25.0] || -> .
% 0.41/0.61 1107[4:Spt:1102.0,515.1,517.0] || cycle(e_1,e_2)*+ -> .
% 0.41/0.61 1108[4:Spt:1102.0,515.0,515.2,515.3] || greater(e_0,e_0)+ -> cycle(e_1,e_1) equalish(e_0,e_2)*.
% 0.41/0.61 1110[4:MRR:164.1,1107.0] || greater(e_0,e_0) -> cycle(e_1,e_1) product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 0.41/0.61 1114[5:Spt:1108.1] || -> cycle(e_1,e_1)*.
% 0.41/0.61 1121[5:Res:1114.0,506.0] || greater(e_1,e_0) -> equalish(e_1,e_2)*.
% 0.41/0.61 1122[5:MRR:1121.0,1121.1,4.0,20.0] || -> .
% 0.41/0.61 1123[5:Spt:1122.0,1108.1,1114.0] || cycle(e_1,e_1)*+ -> .
% 0.41/0.61 1124[5:Spt:1122.0,1108.0,1108.2] || greater(e_0,e_0)+ -> equalish(e_0,e_2)*.
% 0.41/0.61 1126[5:MRR:1110.1,1123.0] || greater(e_0,e_0)+ -> product(e_1,e_1,e_3) product(e_1,e_1,e_2)*.
% 0.41/0.61 1127[6:Spt:532.0] || -> product(e_2,e_1,e_3)*.
% 0.41/0.61 1131[6:Res:1127.0,28.0] || product(e_2,u,e_3)*+ -> equalish(u,e_1).
% 0.41/0.61 1132[6:Res:1127.0,29.0] || product(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.41/0.61 1135[6:Res:1127.0,42.2] group_element(e_3) group_element(e_2) || -> product(e_2,e_3,e_3) product(e_2,e_3,e_2) product(e_1,e_1,e_2)*.
% 0.41/0.61 1138[6:SSi:1135.1,1135.0,18.0,19.0] || -> product(e_2,e_3,e_3) product(e_2,e_3,e_2) product(e_1,e_1,e_2)*.
% 0.41/0.61 1168[7:Spt:1126.1] || -> product(e_1,e_1,e_3)*.
% 0.41/0.61 1174[7:Res:1168.0,1132.0] || -> equalish(e_1,e_2)*.
% 0.41/0.61 1178[7:MRR:1174.0,20.0] || -> .
% 0.41/0.61 1182[7:Spt:1178.0,1126.1,1168.0] || product(e_1,e_1,e_3)*+ -> .
% 0.41/0.61 1183[7:Spt:1178.0,1126.0,1126.2] || greater(e_0,e_0)+ -> product(e_1,e_1,e_2)*.
% 0.41/0.61 1191[8:Spt:1138.2] || -> product(e_1,e_1,e_2)*.
% 0.41/0.61 1192[8:Res:1191.0,15.2] || greater(e_2,e_1)* cycle(e_1,e_0) -> .
% 0.41/0.61 1200[8:MRR:1192.0,7.0] || cycle(e_1,e_0)*+ -> .
% 0.41/0.61 1203[8:Res:11.3,1200.0] group_element(e_1) || -> cycle(e_1,e_2) cycle(e_1,e_1)*.
% 0.41/0.61 1204[8:SSi:1203.0,17.0] || -> cycle(e_1,e_2) cycle(e_1,e_1)*.
% 0.41/0.61 1205[8:MRR:1204.0,1204.1,1107.0,1123.0] || -> .
% 0.41/0.61 1206[8:Spt:1205.0,1138.2,1191.0] || product(e_1,e_1,e_2)*+ -> .
% 0.41/0.61 1207[8:Spt:1205.0,1138.0,1138.1] || -> product(e_2,e_3,e_3) product(e_2,e_3,e_2)*.
% 0.41/0.61 1213[8:Res:1207.1,30.0] || product(e_2,u,e_3) -> product(e_2,e_3,e_3)* product(e_2,u,e_2)*.
% 0.41/0.61 1215[8:Res:1207.1,28.0] || product(e_2,u,e_2)* -> product(e_2,e_3,e_3)* equalish(u,e_3).
% 0.41/0.61 1216[8:Res:1207.1,29.0] || product(u,e_3,e_2)* -> product(e_2,e_3,e_3)* equalish(u,e_2).
% 0.41/0.61 1218[8:Res:1207.1,42.2] group_element(e_2) group_element(e_2) || -> product(e_2,e_3,e_3) product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_1,e_3,e_2)*.
% 0.41/0.61 1220[8:Obv:1218.0] group_element(e_2) || -> product(e_2,e_3,e_3) product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_1,e_3,e_2)*.
% 0.41/0.61 1221[8:SSi:1220.0,18.0] || -> product(e_2,e_3,e_3) product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_1,e_3,e_2)*.
% 0.41/0.61 1222[8:MRR:1221.1,1213.0] || -> product(e_2,e_3,e_3) product(e_2,e_2,e_2) product(e_1,e_3,e_2)*.
% 0.41/0.61 1243[9:Spt:1222.0] || -> product(e_2,e_3,e_3)*.
% 0.41/0.61 1250[9:Res:1243.0,1131.0] || -> equalish(e_3,e_1)*.
% 0.41/0.61 1251[9:MRR:1250.0,24.0] || -> .
% 0.41/0.61 1253[9:Spt:1251.0,1222.0,1243.0] || product(e_2,e_3,e_3)*+ -> .
% 0.41/0.61 1254[9:Spt:1251.0,1222.1,1222.2] || -> product(e_2,e_2,e_2) product(e_1,e_3,e_2)*.
% 0.41/0.61 1257[9:MRR:1215.1,1253.0] || product(e_2,u,e_2)*+ -> equalish(u,e_3).
% 0.41/0.61 1258[9:MRR:1216.1,1253.0] || product(u,e_3,e_2)*+ -> equalish(u,e_2).
% 0.41/0.61 1314[9:Res:1254.1,1258.0] || -> product(e_2,e_2,e_2)* equalish(e_1,e_2).
% 0.41/0.61 1319[9:MRR:1314.1,20.0] || -> product(e_2,e_2,e_2)*.
% 0.41/0.61 1333[9:Res:1319.0,1257.0] || -> equalish(e_2,e_3)*.
% 0.41/0.61 1334[9:MRR:1333.0,23.0] || -> .
% 0.41/0.61 1337[6:Spt:1334.0,532.0,1127.0] || product(e_2,e_1,e_3)*+ -> .
% 0.41/0.61 1338[6:Spt:1334.0,532.1] || -> product(e_2,e_1,e_2)*.
% 0.41/0.61 1339[6:MRR:537.1,1337.0] || product(u,e_1,e_2)*+ -> equalish(u,e_2).
% 0.41/0.61 1340[6:MRR:536.1,1337.0] || product(e_2,u,e_2)*+ -> equalish(u,e_1).
% 0.41/0.61 1344[6:MRR:543.0,1337.0] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_1,e_1,e_2)*.
% 0.41/0.61 1375[7:Spt:155.3] || -> product(e_1,e_1,e_2)*.
% 0.41/0.61 1381[7:Res:1375.0,1339.0] || -> equalish(e_1,e_2)*.
% 0.41/0.61 1385[7:MRR:1381.0,20.0] || -> .
% 0.41/0.61 1390[7:Spt:1385.0,155.3,1375.0] || product(e_1,e_1,e_2)*+ -> .
% 0.41/0.61 1391[7:Spt:1385.0,155.0,155.1,155.2] || cycle(e_1,u)+ greater(u,e_0)* -> product(e_1,e_1,e_3)*.
% 0.41/0.61 1393[7:MRR:1344.2,1390.0] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)*.
% 0.41/0.61 1431[7:Res:1393.1,1340.0] || -> product(e_2,e_2,e_3)* equalish(e_2,e_1).
% 0.41/0.61 1432[7:MRR:1431.1,22.0] || -> product(e_2,e_2,e_3)*.
% 0.41/0.61 1438[7:Res:1432.0,30.0] || product(e_2,u,e_2)*+ -> product(e_3,u,e_2).
% 0.41/0.61 1498[7:Res:1338.0,1438.0] || -> product(e_3,e_1,e_2)*.
% 0.41/0.61 1507[7:Res:1498.0,1339.0] || -> equalish(e_3,e_2)*.
% 0.41/0.61 1511[7:MRR:1507.0,25.0] || -> .
% 0.41/0.61 1514[3:Spt:1511.0,501.1,504.0] || cycle(e_2,e_1)*+ -> .
% 0.41/0.61 1515[3:Spt:1511.0,501.0,501.2] || greater(e_0,e_0)+ -> equalish(e_0,e_1)*.
% 0.41/0.61 1516[3:MRR:502.2,1514.0] || cycle(e_1,u)+ greater(u,e_0) -> equalish(u,e_1)*.
% 0.41/0.61 1517[3:MRR:503.1,1514.0] || greater(e_0,e_0)+ -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.41/0.61 1520[4:Spt:1517.1] || -> product(e_2,e_1,e_3)*.
% 0.41/0.61 1521[4:Res:1520.0,15.2] || greater(e_3,e_2)* cycle(e_2,e_0) -> .
% 0.41/0.61 1529[4:MRR:1521.0,9.0] || cycle(e_2,e_0)*+ -> .
% 0.41/0.61 1532[4:Res:11.3,1529.0] group_element(e_2) || -> cycle(e_2,e_2) cycle(e_2,e_1)*.
% 0.41/0.61 1533[4:SSi:1532.0,18.0] || -> cycle(e_2,e_2) cycle(e_2,e_1)*.
% 0.41/0.61 1534[4:MRR:1533.0,1533.1,500.0,1514.0] || -> .
% 0.41/0.61 1535[4:Spt:1534.0,1517.1,1520.0] || product(e_2,e_1,e_3)*+ -> .
% 0.41/0.61 1536[4:Spt:1534.0,1517.0,1517.2] || greater(e_0,e_0)+ -> product(e_2,e_1,e_2)*.
% 0.41/0.61 1540[5:Spt:155.3] || -> product(e_1,e_1,e_2)*.
% 0.41/0.61 1541[5:Res:1540.0,15.2] || greater(e_2,e_1)* cycle(e_1,e_0) -> .
% 0.41/0.61 1549[5:MRR:1541.0,7.0] || cycle(e_1,e_0)*+ -> .
% 0.41/0.61 1552[5:Res:11.3,1549.0] group_element(e_1) || -> cycle(e_1,e_2) cycle(e_1,e_1)*.
% 0.41/0.61 1553[5:SSi:1552.0,17.0] || -> cycle(e_1,e_2) cycle(e_1,e_1)*.
% 0.41/0.61 1554[6:Spt:1553.0] || -> cycle(e_1,e_2)*.
% 0.41/0.61 1561[6:Res:1554.0,1516.0] || greater(e_2,e_0) -> equalish(e_2,e_1)*.
% 0.41/0.61 1562[6:MRR:1561.0,1561.1,5.0,22.0] || -> .
% 0.41/0.61 1563[6:Spt:1562.0,1553.0,1554.0] || cycle(e_1,e_2)*+ -> .
% 0.41/0.61 1564[6:Spt:1562.0,1553.1] || -> cycle(e_1,e_1)*.
% 0.41/0.61 1566[6:MRR:89.0,1564.0] || cycle(e_2,e_0)*+ -> .
% 0.41/0.61 1571[6:Res:11.3,1566.0] group_element(e_2) || -> cycle(e_2,e_2) cycle(e_2,e_1)*.
% 0.41/0.61 1572[6:SSi:1571.0,18.0] || -> cycle(e_2,e_2) cycle(e_2,e_1)*.
% 0.41/0.61 1573[6:MRR:1572.0,1572.1,500.0,1514.0] || -> .
% 0.41/0.61 1574[5:Spt:1573.0,155.3,1540.0] || product(e_1,e_1,e_2)*+ -> .
% 0.41/0.61 1575[5:Spt:1573.0,155.0,155.1,155.2] || cycle(e_1,u)+ greater(u,e_0)* -> product(e_1,e_1,e_3)*.
% 0.41/0.61 1587[5:Res:610.3,1574.0] group_element(e_2) || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.41/0.61 1590[5:SSi:1587.0,18.0] || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.41/0.61 1591[5:MRR:1590.0,1535.0] || -> product(e_2,e_1,e_2)*.
% 0.41/0.61 1603[5:Res:1591.0,28.0] || product(e_2,u,e_2)*+ -> equalish(u,e_1).
% 0.41/0.61 1604[5:Res:1591.0,29.0] || product(u,e_1,e_2)*+ -> equalish(u,e_2).
% 0.41/0.61 1607[5:Res:1591.0,42.2] group_element(e_2) group_element(e_2) || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_1,e_1,e_2)*.
% 0.41/0.61 1609[5:Obv:1607.0] group_element(e_2) || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_1,e_1,e_2)*.
% 0.41/0.61 1610[5:SSi:1609.0,18.0] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2) product(e_1,e_1,e_2)*.
% 0.41/0.61 1611[5:MRR:1610.2,1574.0] || -> product(e_2,e_2,e_3) product(e_2,e_2,e_2)*.
% 0.41/0.61 1636[5:Res:1611.1,1603.0] || -> product(e_2,e_2,e_3)* equalish(e_2,e_1).
% 0.41/0.61 1637[5:MRR:1636.1,22.0] || -> product(e_2,e_2,e_3)*.
% 0.41/0.61 1643[5:Res:1637.0,30.0] || product(e_2,u,e_2)*+ -> product(e_3,u,e_2).
% 0.41/0.61 1697[5:Res:1591.0,1643.0] || -> product(e_3,e_1,e_2)*.
% 0.41/0.61 1706[5:Res:1697.0,1604.0] || -> equalish(e_3,e_2)*.
% 0.41/0.61 1710[5:MRR:1706.0,25.0] || -> .
% 0.41/0.61 % SZS output end Refutation
% 0.41/0.61 Formulae used in the proof : e_0_then_e_1 e_1_then_e_2 e_2_then_e_3 e_1_greater_e_0 e_2_greater_e_0 e_2_greater_e_1 e_3_greater_e_1 e_3_greater_e_2 cycle2 cycle3 cycle4 cycle5 cycle6 cycle7 element_1 element_2 element_3 e_1_is_not_e_2 e_1_is_not_e_3 e_2_is_not_e_1 e_2_is_not_e_3 e_3_is_not_e_1 e_3_is_not_e_2 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation qg3
% 0.41/0.61
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