TSTP Solution File: GRP130-2.003 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP130-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:45:46 EDT 2022
% Result : Unsatisfiable 0.38s 0.58s
% Output : Refutation 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP130-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n013.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 : Mon Jun 13 06:00:59 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.38/0.58
% 0.38/0.58 SPASS V 3.9
% 0.38/0.58 SPASS beiseite: Proof found.
% 0.38/0.58 % SZS status Theorem
% 0.38/0.58 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.58 SPASS derived 803 clauses, backtracked 104 clauses, performed 13 splits and kept 606 clauses.
% 0.38/0.58 SPASS allocated 76516 KBytes.
% 0.38/0.58 SPASS spent 0:00:00.24 on the problem.
% 0.38/0.58 0:00:00.03 for the input.
% 0.38/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.38/0.58 0:00:00.01 for inferences.
% 0.38/0.58 0:00:00.00 for the backtracking.
% 0.38/0.58 0:00:00.16 for the reduction.
% 0.38/0.58
% 0.38/0.58
% 0.38/0.58 Here is a proof with depth 13, length 173 :
% 0.38/0.58 % SZS output start Refutation
% 0.38/0.58 1[0:Inp] || -> next(e_1,e_2)*.
% 0.38/0.58 5[0:Inp] || -> greater(e_3,e_2)*.
% 0.38/0.58 6[0:Inp] || greater(u,v)* next(w,v)* product(w,e_1,u)*+ -> .
% 0.38/0.58 7[0:Inp] || -> group_element(e_1)*.
% 0.38/0.58 8[0:Inp] || -> group_element(e_2)*.
% 0.38/0.58 9[0:Inp] || -> group_element(e_3)*.
% 0.38/0.58 10[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.38/0.58 11[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.38/0.58 12[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.38/0.58 13[0:Inp] || equalish(e_2,e_3)*+ -> .
% 0.38/0.58 14[0:Inp] || equalish(e_3,e_1)*+ -> .
% 0.38/0.58 15[0:Inp] || equalish(e_3,e_2)*+ -> .
% 0.38/0.58 16[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 0.38/0.58 17[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.38/0.58 18[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.38/0.58 19[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.38/0.58 20[0:Inp] || product(u,v,w)*+ product(u,x,v)* -> product(w,x,u)*.
% 0.38/0.58 25[0:Res:16.4,20.0] 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)*.
% 0.38/0.58 26[0:Res:16.4,17.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_3) product(v,u,e_2)* equalish(w,e_1).
% 0.38/0.58 34[0:Res:16.4,26.2] 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).
% 0.38/0.58 35[0:Obv:34.5] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)* equalish(e_1,e_1).
% 0.38/0.58 36[0:Res:16.4,25.2] 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)*.
% 0.38/0.58 37[0:Obv:36.1] 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)*.
% 0.38/0.58 38[0:SSi:37.1,7.0] 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)*.
% 0.38/0.58 39[1:Spt:35.0,35.1,35.2,35.3] group_element(u) group_element(v) || -> product(v,u,e_3) product(v,u,e_2)*.
% 0.38/0.58 41[1:Res:39.3,20.0] group_element(u) group_element(v) || product(v,w,u)*+ -> product(v,u,e_3)* product(e_2,w,v)*.
% 0.38/0.58 42[1:Res:39.3,17.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_3)* equalish(w,e_2).
% 0.38/0.58 43[1:Res:39.3,18.0] group_element(u) group_element(v) || product(v,w,e_2)*+ -> product(v,u,e_3)* equalish(w,u)*.
% 0.38/0.58 47[1:Res:39.3,42.2] group_element(u) group_element(v) group_element(u) group_element(v) || -> product(v,u,e_3)* product(v,u,e_3)* equalish(e_2,e_2).
% 0.38/0.58 48[1:Obv:47.4] group_element(u) group_element(v) || -> product(v,u,e_3)* equalish(e_2,e_2).
% 0.38/0.58 51[2:Spt:48.0,48.1,48.2] group_element(u) group_element(v) || -> product(v,u,e_3)*.
% 0.38/0.58 52[2:Res:51.2,6.2] group_element(e_1) group_element(u) || greater(e_3,v) next(u,v)* -> .
% 0.38/0.58 57[2:SSi:52.0,7.0] group_element(u) || greater(e_3,v)+ next(u,v)* -> .
% 0.38/0.58 58[2:Res:5.0,57.1] group_element(u) || next(u,e_2)*+ -> .
% 0.38/0.58 60[2:Res:1.0,58.1] group_element(e_1) || -> .
% 0.38/0.58 61[2:SSi:60.0,7.0] || -> .
% 0.38/0.58 62[2:Spt:61.0,48.3] || -> equalish(e_2,e_2)*.
% 0.38/0.58 74[1:Res:39.3,41.2] group_element(u) group_element(v) group_element(e_2) group_element(v) || -> product(v,u,e_3)* product(v,e_2,e_3)* product(e_2,u,v)*.
% 0.38/0.58 75[1:Obv:74.1] group_element(u) group_element(e_2) group_element(v) || -> product(v,u,e_3)* product(v,e_2,e_3)* product(e_2,u,v)*.
% 0.38/0.58 76[1:SSi:75.1,8.0] group_element(u) group_element(v) || -> product(v,u,e_3)* product(v,e_2,e_3)* product(e_2,u,v)*.
% 0.38/0.58 77[1:Fac:76.2,76.3] group_element(e_2) group_element(u) || -> product(u,e_2,e_3)* product(e_2,e_2,u)*.
% 0.38/0.58 100[1:SSi:77.0,8.0] group_element(u) || -> product(u,e_2,e_3)* product(e_2,e_2,u)*.
% 0.38/0.58 119[1:Res:100.1,41.2] group_element(u) group_element(e_3) group_element(u) || -> product(e_2,e_2,u)* product(u,e_3,e_3)* product(e_2,e_2,u)*.
% 0.38/0.58 125[1:Res:100.2,42.2] group_element(u) group_element(e_2) group_element(e_2) || -> product(u,e_2,e_3)* product(e_2,e_2,e_3)* equalish(u,e_2).
% 0.38/0.58 126[1:Res:100.2,43.2] group_element(e_2) group_element(u) group_element(e_2) || -> product(e_2,e_2,e_3)* product(e_2,u,e_3)* equalish(e_2,u).
% 0.38/0.58 128[1:Obv:126.0] group_element(u) group_element(e_2) || -> product(e_2,e_2,e_3)* product(e_2,u,e_3)* equalish(e_2,u).
% 0.38/0.58 129[1:SSi:128.1,8.0] group_element(u) || -> product(e_2,e_2,e_3)* product(e_2,u,e_3)* equalish(e_2,u).
% 0.38/0.58 130[1:Obv:125.1] group_element(u) group_element(e_2) || -> product(u,e_2,e_3)* product(e_2,e_2,e_3)* equalish(u,e_2).
% 0.38/0.58 131[1:SSi:130.1,8.0] group_element(u) || -> product(u,e_2,e_3)* product(e_2,e_2,e_3)* equalish(u,e_2).
% 0.38/0.58 137[1:Obv:119.3] group_element(e_3) group_element(u) || -> product(u,e_3,e_3)* product(e_2,e_2,u)*.
% 0.38/0.58 138[1:SSi:137.0,9.0] group_element(u) || -> product(u,e_3,e_3)* product(e_2,e_2,u)*.
% 0.38/0.58 150[1:Res:138.2,42.2] group_element(u) group_element(e_2) group_element(e_2) || -> product(u,e_3,e_3)* product(e_2,e_2,e_3)* equalish(u,e_2).
% 0.38/0.58 155[1:Obv:150.1] group_element(u) group_element(e_2) || -> product(u,e_3,e_3)* product(e_2,e_2,e_3)* equalish(u,e_2).
% 0.38/0.58 156[1:SSi:155.1,8.0] group_element(u) || -> product(u,e_3,e_3)* product(e_2,e_2,e_3)* equalish(u,e_2).
% 0.38/0.58 163[3:Spt:129.0,129.2,129.3] group_element(u) || -> product(e_2,u,e_3)* equalish(e_2,u).
% 0.38/0.58 170[3:Res:163.1,41.2] group_element(u) group_element(e_3) group_element(e_2) || -> equalish(e_2,u) product(e_2,e_3,e_3)* product(e_2,u,e_2)*.
% 0.38/0.58 174[3:SSi:170.2,170.1,8.0,9.0] group_element(u) || -> equalish(e_2,u) product(e_2,e_3,e_3)* product(e_2,u,e_2)*.
% 0.38/0.58 212[4:Spt:131.0,131.1,131.3] group_element(u) || -> product(u,e_2,e_3)* equalish(u,e_2).
% 0.38/0.58 264[5:Spt:156.0,156.1,156.3] group_element(u) || -> product(u,e_3,e_3)* equalish(u,e_2).
% 0.38/0.58 273[6:Spt:174.0,174.1,174.3] group_element(u) || -> equalish(e_2,u) product(e_2,u,e_2)*.
% 0.38/0.58 276[6:Res:273.2,20.0] group_element(u) || product(e_2,v,u)* -> equalish(e_2,u) product(e_2,v,e_2)*.
% 0.38/0.58 285[6:MRR:276.3,17.1] group_element(u) || product(e_2,v,u)*+ -> equalish(e_2,u).
% 0.38/0.58 332[6:Res:163.1,285.1] group_element(u) group_element(e_3) || -> equalish(e_2,u)* equalish(e_2,e_3)*.
% 0.38/0.58 334[6:Con:332.0] group_element(e_3) || -> equalish(e_2,e_3)*.
% 0.38/0.58 335[6:SSi:334.0,9.0] || -> equalish(e_2,e_3)*.
% 0.38/0.58 336[6:MRR:335.0,13.0] || -> .
% 0.38/0.58 355[6:Spt:336.0,174.2] || -> product(e_2,e_3,e_3)*.
% 0.38/0.58 359[6:Res:355.0,19.0] || product(u,e_3,e_3)* -> equalish(u,e_2).
% 0.38/0.58 362[6:MRR:264.1,359.0] group_element(u) || -> equalish(u,e_2)*.
% 0.38/0.58 364[6:Res:362.1,10.0] group_element(e_1) || -> .
% 0.38/0.58 366[6:SSi:364.0,7.0] || -> .
% 0.38/0.58 367[5:Spt:366.0,156.2] || -> product(e_2,e_2,e_3)*.
% 0.38/0.58 371[5:Res:367.0,19.0] || product(u,e_2,e_3)* -> equalish(u,e_2).
% 0.38/0.58 374[5:MRR:212.1,371.0] group_element(u) || -> equalish(u,e_2)*.
% 0.38/0.58 377[5:Res:374.1,10.0] group_element(e_1) || -> .
% 0.38/0.58 379[5:SSi:377.0,7.0] || -> .
% 0.38/0.58 380[4:Spt:379.0,131.2] || -> product(e_2,e_2,e_3)*.
% 0.38/0.58 382[4:Res:380.0,20.0] || product(e_2,u,e_2)*+ -> product(e_3,u,e_2).
% 0.38/0.58 384[4:Res:380.0,18.0] || product(e_2,u,e_3)*+ -> equalish(u,e_2).
% 0.38/0.58 475[4:Res:39.3,382.0] group_element(u) group_element(e_2) || -> product(e_2,u,e_3)* product(e_3,u,e_2).
% 0.38/0.58 478[4:Res:138.2,382.0] group_element(e_2) || -> product(e_2,e_3,e_3)* product(e_3,e_2,e_2).
% 0.38/0.58 480[4:SSi:478.0,8.0] || -> product(e_2,e_3,e_3)* product(e_3,e_2,e_2).
% 0.38/0.58 481[4:SSi:475.1,8.0] group_element(u) || -> product(e_2,u,e_3)* product(e_3,u,e_2).
% 0.38/0.58 482[5:Spt:480.0] || -> product(e_2,e_3,e_3)*.
% 0.38/0.58 489[5:Res:482.0,384.0] || -> equalish(e_3,e_2)*.
% 0.38/0.58 490[5:MRR:489.0,15.0] || -> .
% 0.38/0.58 494[5:Spt:490.0,480.0,482.0] || product(e_2,e_3,e_3)*+ -> .
% 0.38/0.58 495[5:Spt:490.0,480.1] || -> product(e_3,e_2,e_2)*.
% 0.38/0.58 499[5:Res:495.0,20.0] || product(e_3,u,e_2) -> product(e_2,u,e_3)*.
% 0.38/0.58 506[5:MRR:481.2,499.0] group_element(u) || -> product(e_2,u,e_3)*.
% 0.38/0.58 532[5:Res:506.1,494.0] group_element(e_3) || -> .
% 0.38/0.58 533[5:SSi:532.0,9.0] || -> .
% 0.38/0.58 535[3:Spt:533.0,129.1] || -> product(e_2,e_2,e_3)*.
% 0.38/0.58 536[3:Res:535.0,20.0] || product(e_2,u,e_2)*+ -> product(e_3,u,e_2).
% 0.38/0.59 538[3:Res:535.0,18.0] || product(e_2,u,e_3)*+ -> equalish(u,e_2).
% 0.38/0.59 613[3:Res:39.3,536.0] group_element(u) group_element(e_2) || -> product(e_2,u,e_3)* product(e_3,u,e_2).
% 0.38/0.59 616[3:Res:138.2,536.0] group_element(e_2) || -> product(e_2,e_3,e_3)* product(e_3,e_2,e_2).
% 0.38/0.59 618[3:SSi:616.0,8.0] || -> product(e_2,e_3,e_3)* product(e_3,e_2,e_2).
% 0.38/0.59 619[3:SSi:613.1,8.0] group_element(u) || -> product(e_2,u,e_3)* product(e_3,u,e_2).
% 0.38/0.59 620[4:Spt:618.0] || -> product(e_2,e_3,e_3)*.
% 0.38/0.59 627[4:Res:620.0,538.0] || -> equalish(e_3,e_2)*.
% 0.38/0.59 628[4:MRR:627.0,15.0] || -> .
% 0.38/0.59 632[4:Spt:628.0,618.0,620.0] || product(e_2,e_3,e_3)*+ -> .
% 0.38/0.59 633[4:Spt:628.0,618.1] || -> product(e_3,e_2,e_2)*.
% 0.38/0.59 637[4:Res:633.0,20.0] || product(e_3,u,e_2) -> product(e_2,u,e_3)*.
% 0.38/0.59 644[4:MRR:619.2,637.0] group_element(u) || -> product(e_2,u,e_3)*.
% 0.38/0.59 670[4:Res:644.1,632.0] group_element(e_3) || -> .
% 0.38/0.59 671[4:SSi:670.0,9.0] || -> .
% 0.38/0.59 674[1:Spt:671.0,35.4] || -> equalish(e_1,e_1)*.
% 0.38/0.59 688[0:Fac:38.3,38.5] 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)*.
% 0.38/0.59 702[0:Res:38.6,6.2] group_element(e_1) group_element(u) || greater(u,v)* next(e_1,v)* -> product(u,e_1,e_3) product(u,e_1,e_2)* product(u,e_1,e_3) product(u,e_1,e_2)*.
% 0.38/0.59 711[0:Obv:688.2] 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)*.
% 0.38/0.59 712[0:SSi:711.0,7.0] group_element(u) || -> product(u,e_1,e_3) product(u,e_1,e_2)* product(e_1,e_1,u)*.
% 0.38/0.59 713[0:Obv:702.5] group_element(e_1) group_element(u) || greater(u,v)* next(e_1,v)* -> product(u,e_1,e_3) product(u,e_1,e_2)*.
% 0.38/0.59 714[0:SSi:713.0,7.0] group_element(u) || greater(u,v)*+ next(e_1,v)* -> product(u,e_1,e_3) product(u,e_1,e_2)*.
% 0.38/0.59 732[0:Res:712.2,25.2] group_element(u) group_element(e_2) group_element(u) || -> product(u,e_1,e_3)* product(e_1,e_1,u)* product(u,e_2,e_3) product(u,e_2,e_2) product(e_1,e_1,u)*.
% 0.38/0.59 751[0:Obv:732.4] group_element(e_2) group_element(u) || -> product(u,e_1,e_3)* product(u,e_2,e_3) product(u,e_2,e_2) product(e_1,e_1,u)*.
% 0.38/0.59 752[0:SSi:751.0,8.0] group_element(u) || -> product(u,e_1,e_3)* product(u,e_2,e_3) product(u,e_2,e_2) product(e_1,e_1,u)*.
% 0.38/0.59 780[0:Res:5.0,714.1] group_element(e_3) || next(e_1,e_2) -> product(e_3,e_1,e_3) product(e_3,e_1,e_2)*.
% 0.38/0.59 783[0:SSi:780.0,9.0] || next(e_1,e_2) -> product(e_3,e_1,e_3) product(e_3,e_1,e_2)*.
% 0.38/0.59 784[0:MRR:783.0,1.0] || -> product(e_3,e_1,e_3) product(e_3,e_1,e_2)*.
% 0.38/0.59 788[0:Res:784.1,17.0] || product(e_3,e_1,u)*+ -> product(e_3,e_1,e_3)* equalish(u,e_2).
% 0.38/0.59 789[0:Res:784.1,18.0] || product(e_3,u,e_2)* -> product(e_3,e_1,e_3)* equalish(u,e_1).
% 0.38/0.59 790[0:Res:784.1,19.0] || product(u,e_1,e_2)* -> product(e_3,e_1,e_3)* equalish(u,e_3).
% 0.38/0.59 819[2:Spt:788.1] || -> product(e_3,e_1,e_3)*.
% 0.38/0.59 823[2:Res:819.0,18.0] || product(e_3,u,e_3)*+ -> equalish(u,e_1).
% 0.38/0.59 824[2:Res:819.0,19.0] || product(u,e_1,e_3)*+ -> equalish(u,e_3).
% 0.38/0.59 826[2:Res:819.0,25.2] group_element(e_3) group_element(e_3) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_1,e_1,e_3)*.
% 0.38/0.59 827[2:Obv:826.0] group_element(e_3) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_1,e_1,e_3)*.
% 0.38/0.59 828[2:SSi:827.0,9.0] || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_1,e_1,e_3)*.
% 0.38/0.59 902[3:Spt:828.0] || -> product(e_3,e_3,e_3)*.
% 0.38/0.59 909[3:Res:902.0,823.0] || -> equalish(e_3,e_1)*.
% 0.38/0.59 910[3:MRR:909.0,14.0] || -> .
% 0.38/0.59 913[3:Spt:910.0,828.0,902.0] || product(e_3,e_3,e_3)*+ -> .
% 0.38/0.59 914[3:Spt:910.0,828.1,828.2] || -> product(e_3,e_3,e_2) product(e_1,e_1,e_3)*.
% 0.38/0.59 915[4:Spt:914.0] || -> product(e_3,e_3,e_2)*.
% 0.38/0.59 916[4:Res:915.0,20.0] || product(e_3,u,e_3)+ -> product(e_2,u,e_3)*.
% 0.38/0.59 964[4:Res:819.0,916.0] || -> product(e_2,e_1,e_3)*.
% 0.38/0.59 971[4:Res:964.0,824.0] || -> equalish(e_2,e_3)*.
% 0.38/0.59 974[4:MRR:971.0,13.0] || -> .
% 0.38/0.59 976[4:Spt:974.0,914.0,915.0] || product(e_3,e_3,e_2)* -> .
% 0.38/0.59 977[4:Spt:974.0,914.1] || -> product(e_1,e_1,e_3)*.
% 0.38/0.59 983[4:Res:977.0,824.0] || -> equalish(e_1,e_3)*.
% 0.38/0.59 986[4:MRR:983.0,11.0] || -> .
% 0.38/0.59 990[2:Spt:986.0,788.1,819.0] || product(e_3,e_1,e_3)*+ -> .
% 0.38/0.59 991[2:Spt:986.0,788.0,788.2] || product(e_3,e_1,u)*+ -> equalish(u,e_2).
% 0.38/0.59 995[2:MRR:789.1,990.0] || product(e_3,u,e_2)*+ -> equalish(u,e_1).
% 0.38/0.59 996[2:MRR:790.1,990.0] || product(u,e_1,e_2)*+ -> equalish(u,e_3).
% 0.38/0.59 1048[2:Res:712.3,996.0] group_element(e_2) || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)* equalish(e_1,e_3).
% 0.38/0.59 1050[2:SSi:1048.0,8.0] || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)* equalish(e_1,e_3).
% 0.38/0.59 1051[2:MRR:1050.2,11.0] || -> product(e_2,e_1,e_3) product(e_2,e_1,e_2)*.
% 0.38/0.59 1066[2:Res:1051.1,996.0] || -> product(e_2,e_1,e_3)* equalish(e_2,e_3).
% 0.38/0.59 1069[2:MRR:1066.1,13.0] || -> product(e_2,e_1,e_3)*.
% 0.38/0.59 1076[2:Res:1069.0,19.0] || product(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.38/0.59 1094[2:Res:752.4,1076.0] group_element(e_3) || -> product(e_3,e_1,e_3)* product(e_3,e_2,e_3) product(e_3,e_2,e_2) equalish(e_1,e_2).
% 0.38/0.59 1097[2:SSi:1094.0,9.0] || -> product(e_3,e_1,e_3)* product(e_3,e_2,e_3) product(e_3,e_2,e_2) equalish(e_1,e_2).
% 0.38/0.59 1098[2:MRR:1097.0,1097.3,990.0,10.0] || -> product(e_3,e_2,e_3) product(e_3,e_2,e_2)*.
% 0.38/0.59 1147[2:Res:1098.1,995.0] || -> product(e_3,e_2,e_3)* equalish(e_2,e_1).
% 0.38/0.59 1148[2:MRR:1147.1,12.0] || -> product(e_3,e_2,e_3)*.
% 0.38/0.59 1151[2:Res:1148.0,20.0] || product(e_3,u,e_2)* -> product(e_3,u,e_3).
% 0.38/0.59 1153[2:Res:1148.0,18.0] || product(e_3,u,e_3)*+ -> equalish(u,e_2).
% 0.38/0.59 1154[2:Res:1148.0,19.0] || product(u,e_2,e_3)*+ -> equalish(u,e_3).
% 0.38/0.59 1156[2:Res:1148.0,25.2] group_element(e_3) group_element(e_3) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_1,e_2,e_3)*.
% 0.38/0.59 1160[2:Obv:1156.0] group_element(e_3) || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_1,e_2,e_3)*.
% 0.38/0.59 1161[2:SSi:1160.0,9.0] || -> product(e_3,e_3,e_3) product(e_3,e_3,e_2) product(e_1,e_2,e_3)*.
% 0.38/0.59 1162[2:MRR:1161.1,1151.0] || -> product(e_3,e_3,e_3) product(e_1,e_2,e_3)*.
% 0.38/0.59 1163[3:Spt:1162.0] || -> product(e_3,e_3,e_3)*.
% 0.38/0.59 1222[3:Res:1163.0,1153.0] || -> equalish(e_3,e_2)*.
% 0.38/0.59 1223[3:MRR:1222.0,15.0] || -> .
% 0.38/0.59 1224[3:Spt:1223.0,1162.0,1163.0] || product(e_3,e_3,e_3)*+ -> .
% 0.38/0.59 1225[3:Spt:1223.0,1162.1] || -> product(e_1,e_2,e_3)*.
% 0.38/0.59 1238[3:Res:1225.0,1154.0] || -> equalish(e_1,e_3)*.
% 0.38/0.59 1240[3:MRR:1238.0,11.0] || -> .
% 0.38/0.59 % SZS output end Refutation
% 0.38/0.59 Formulae used in the proof : e_1_then_e_2 e_3_greater_e_2 no_redundancy 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
% 0.38/0.59
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