TSTP Solution File: GRP124-9.004 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP124-9.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:45:34 EDT 2022
% Result : Unsatisfiable 0.65s 0.90s
% Output : Refutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP124-9.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 11:44:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.65/0.90
% 0.65/0.90 SPASS V 3.9
% 0.65/0.90 SPASS beiseite: Proof found.
% 0.65/0.90 % SZS status Theorem
% 0.65/0.90 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.65/0.90 SPASS derived 1952 clauses, backtracked 219 clauses, performed 37 splits and kept 1030 clauses.
% 0.65/0.90 SPASS allocated 77650 KBytes.
% 0.65/0.90 SPASS spent 0:00:00.56 on the problem.
% 0.65/0.90 0:00:00.04 for the input.
% 0.65/0.90 0:00:00.00 for the FLOTTER CNF translation.
% 0.65/0.90 0:00:00.03 for inferences.
% 0.65/0.90 0:00:00.01 for the backtracking.
% 0.65/0.90 0:00:00.44 for the reduction.
% 0.65/0.90
% 0.65/0.90
% 0.65/0.90 Here is a proof with depth 14, length 251 :
% 0.65/0.90 % SZS output start Refutation
% 0.65/0.90 3[0:Inp] || -> group_element(e_1)*.
% 0.65/0.90 4[0:Inp] || -> group_element(e_2)*.
% 0.65/0.90 5[0:Inp] || -> group_element(e_3)*.
% 0.65/0.90 6[0:Inp] || -> group_element(e_4)*.
% 0.65/0.90 7[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.65/0.90 8[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.65/0.90 9[0:Inp] || equalish(e_1,e_4)*+ -> .
% 0.65/0.90 10[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.65/0.90 11[0:Inp] || equalish(e_2,e_3)*+ -> .
% 0.65/0.90 12[0:Inp] || equalish(e_2,e_4)*+ -> .
% 0.65/0.90 13[0:Inp] || equalish(e_3,e_1)*+ -> .
% 0.65/0.90 14[0:Inp] || equalish(e_3,e_2)*+ -> .
% 0.65/0.90 15[0:Inp] || equalish(e_3,e_4)*+ -> .
% 0.65/0.90 16[0:Inp] || equalish(e_4,e_1)*+ -> .
% 0.65/0.90 17[0:Inp] || equalish(e_4,e_2)*+ -> .
% 0.65/0.90 18[0:Inp] || equalish(e_4,e_3)*+ -> .
% 0.65/0.90 19[0:Inp] group_element(u) group_element(v) || -> product1(v,u,e_4) product1(v,u,e_3) product1(v,u,e_2) product1(v,u,e_1)*.
% 0.65/0.90 20[0:Inp] || product1(u,v,w)*+ product1(u,v,x)* -> equalish(x,w)*.
% 0.65/0.90 21[0:Inp] || product1(u,v,w)*+ product1(u,x,w)* -> equalish(x,v)*.
% 0.65/0.90 22[0:Inp] || product1(u,v,w)*+ product1(x,v,w)* -> equalish(x,u)*.
% 0.65/0.90 23[0:Inp] || -> product1(u,u,u)*.
% 0.65/0.90 24[0:Inp] group_element(u) group_element(v) || -> product2(v,u,e_4) product2(v,u,e_3) product2(v,u,e_2) product2(v,u,e_1)*.
% 0.65/0.90 25[0:Inp] || product2(u,v,w)*+ product2(u,v,x)* -> equalish(x,w)*.
% 0.65/0.90 26[0:Inp] || product2(u,v,w)*+ product2(u,x,w)* -> equalish(x,v)*.
% 0.65/0.90 27[0:Inp] || product2(u,v,w)*+ product2(x,v,w)* -> equalish(x,u)*.
% 0.65/0.90 28[0:Inp] || -> product2(u,u,u)*.
% 0.65/0.90 29[0:Inp] || product1(u,v,w)*+ product1(v,x,u)* -> product2(w,x,v)*.
% 0.65/0.90 37[0:Res:28.0,27.0] || product2(u,v,v)*+ -> equalish(u,v).
% 0.65/0.90 40[0:Res:28.0,26.0] || product2(u,v,u)*+ -> equalish(v,u).
% 0.65/0.90 41[0:Res:28.0,25.0] || product2(u,u,v)*+ -> equalish(v,u).
% 0.65/0.90 44[0:Res:23.0,22.0] || product1(u,v,v)*+ -> equalish(u,v).
% 0.65/0.90 46[0:Res:23.0,21.0] || product1(u,v,u)*+ -> equalish(v,u).
% 0.65/0.90 51[0:Res:24.5,40.0] group_element(u) group_element(e_1) || -> product2(e_1,u,e_4) product2(e_1,u,e_3) product2(e_1,u,e_2)* equalish(u,e_1).
% 0.65/0.90 59[0:SSi:51.1,3.0] group_element(u) || -> product2(e_1,u,e_4) product2(e_1,u,e_3) product2(e_1,u,e_2)* equalish(u,e_1).
% 0.65/0.90 70[0:Res:19.5,46.0] group_element(u) group_element(e_1) || -> product1(e_1,u,e_4) product1(e_1,u,e_3) product1(e_1,u,e_2)* equalish(u,e_1).
% 0.65/0.90 74[0:Res:19.5,29.0] group_element(u) group_element(v) || product1(u,w,v)*+ -> product1(v,u,e_4) product1(v,u,e_3) product1(v,u,e_2)* product2(e_1,w,u)*.
% 0.65/0.90 77[0:Res:19.5,22.0] group_element(u) group_element(v) || product1(w,u,e_1)*+ -> product1(v,u,e_4) product1(v,u,e_3) product1(v,u,e_2)* equalish(w,v)*.
% 0.65/0.90 78[0:Res:19.5,44.0] group_element(e_1) group_element(u) || -> product1(u,e_1,e_4) product1(u,e_1,e_3) product1(u,e_1,e_2)* equalish(u,e_1).
% 0.65/0.90 79[0:SSi:78.0,3.0] group_element(u) || -> product1(u,e_1,e_4) product1(u,e_1,e_3) product1(u,e_1,e_2)* equalish(u,e_1).
% 0.65/0.90 81[0:SSi:70.1,3.0] group_element(u) || -> product1(e_1,u,e_4) product1(e_1,u,e_3) product1(e_1,u,e_2)* equalish(u,e_1).
% 0.65/0.90 95[0:Res:59.3,37.0] group_element(e_2) || -> product2(e_1,e_2,e_4) product2(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.65/0.90 97[0:SSi:95.0,4.0] || -> product2(e_1,e_2,e_4) product2(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.65/0.90 98[0:MRR:97.2,97.3,10.0,7.0] || -> product2(e_1,e_2,e_4) product2(e_1,e_2,e_3)*.
% 0.65/0.90 103[0:Res:98.1,25.0] || product2(e_1,e_2,u)*+ -> product2(e_1,e_2,e_4)* equalish(u,e_3).
% 0.65/0.90 106[1:Spt:103.0,103.2] || product2(e_1,e_2,u)*+ -> equalish(u,e_3).
% 0.65/0.90 118[0:Res:79.3,46.0] group_element(e_2) || -> product1(e_2,e_1,e_4) product1(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.65/0.90 124[0:Res:79.3,21.0] group_element(u) || product1(u,v,e_2)*+ -> product1(u,e_1,e_4) product1(u,e_1,e_3)* equalish(u,e_1) equalish(v,e_1).
% 0.65/0.90 126[0:SSi:118.0,4.0] || -> product1(e_2,e_1,e_4) product1(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.65/0.90 127[0:MRR:126.2,126.3,10.0,7.0] || -> product1(e_2,e_1,e_4) product1(e_2,e_1,e_3)*.
% 0.65/0.90 128[0:Res:127.1,29.0] || product1(e_1,u,e_2)+ -> product1(e_2,e_1,e_4) product2(e_3,u,e_1)*.
% 0.65/0.90 129[0:Res:127.1,20.0] || product1(e_2,e_1,u)*+ -> product1(e_2,e_1,e_4)* equalish(u,e_3).
% 0.65/0.90 131[0:Res:127.1,22.0] || product1(u,e_1,e_3)*+ -> product1(e_2,e_1,e_4)* equalish(u,e_2).
% 0.65/0.90 132[2:Spt:129.0,129.2] || product1(e_2,e_1,u)*+ -> equalish(u,e_3).
% 0.65/0.90 150[3:Spt:131.0,131.2] || product1(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.65/0.90 152[4:Spt:128.1] || -> product1(e_2,e_1,e_4)*.
% 0.65/0.90 157[4:Res:152.0,132.0] || -> equalish(e_4,e_3)*.
% 0.65/0.90 158[4:MRR:157.0,18.0] || -> .
% 0.65/0.90 159[4:Spt:158.0,128.1,152.0] || product1(e_2,e_1,e_4)*+ -> .
% 0.65/0.90 160[4:Spt:158.0,128.0,128.2] || product1(e_1,u,e_2)+ -> product2(e_3,u,e_1)*.
% 0.65/0.90 161[4:MRR:127.0,159.0] || -> product1(e_2,e_1,e_3)*.
% 0.65/0.90 170[0:Res:23.0,77.2] group_element(e_1) group_element(u) || -> product1(u,e_1,e_4) product1(u,e_1,e_3) product1(u,e_1,e_2)* equalish(e_1,u).
% 0.65/0.90 172[0:SSi:170.0,3.0] group_element(u) || -> product1(u,e_1,e_4) product1(u,e_1,e_3) product1(u,e_1,e_2)* equalish(e_1,u).
% 0.65/0.90 179[0:Res:81.3,22.0] group_element(u) || product1(v,u,e_2)*+ -> product1(e_1,u,e_4) product1(e_1,u,e_3)* equalish(u,e_1) equalish(v,e_1).
% 0.65/0.90 180[0:Res:81.3,44.0] group_element(e_2) || -> product1(e_1,e_2,e_4) product1(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.65/0.90 181[4:Res:81.3,160.0] group_element(u) || -> product1(e_1,u,e_4) product1(e_1,u,e_3) equalish(u,e_1) product2(e_3,u,e_1)*.
% 0.65/0.90 182[0:SSi:180.0,4.0] || -> product1(e_1,e_2,e_4) product1(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.65/0.90 183[0:MRR:182.2,182.3,10.0,7.0] || -> product1(e_1,e_2,e_4) product1(e_1,e_2,e_3)*.
% 0.65/0.90 187[0:Res:183.1,22.0] || product1(u,e_2,e_3)*+ -> product1(e_1,e_2,e_4)* equalish(u,e_1).
% 0.65/0.90 248[4:Res:181.4,41.0] group_element(e_3) || -> product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)* equalish(e_3,e_1) equalish(e_1,e_3).
% 0.65/0.90 252[4:SSi:248.0,5.0] || -> product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)* equalish(e_3,e_1) equalish(e_1,e_3).
% 0.65/0.90 253[4:MRR:252.1,252.2,252.3,44.0,13.0,8.0] || -> product1(e_1,e_3,e_4)*.
% 0.65/0.90 269[4:Res:161.0,74.2] group_element(e_2) group_element(e_3) || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.65/0.90 272[4:Res:253.0,74.2] group_element(e_1) group_element(e_4) || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2) product2(e_1,e_3,e_1)*.
% 0.65/0.90 273[4:SSi:272.1,272.0,6.0,3.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2) product2(e_1,e_3,e_1)*.
% 0.65/0.90 274[4:SSi:269.1,269.0,5.0,4.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.65/0.90 288[4:Res:273.3,40.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)* equalish(e_3,e_1).
% 0.65/0.90 295[4:MRR:288.3,13.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)*.
% 0.65/0.90 312[4:Res:295.2,20.0] || product1(e_4,e_1,u)*+ -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(u,e_2).
% 0.65/0.90 314[4:Res:295.2,22.0] || product1(u,e_1,e_2)*+ -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(u,e_4).
% 0.65/0.90 321[4:Res:274.3,41.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2)* equalish(e_2,e_1).
% 0.65/0.90 323[4:MRR:321.3,10.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2)*.
% 0.65/0.90 330[4:Res:323.2,44.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)* equalish(e_3,e_2).
% 0.65/0.90 332[4:MRR:330.2,14.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)*.
% 0.65/0.90 334[4:Res:332.1,46.0] || -> product1(e_3,e_2,e_4)* equalish(e_2,e_3).
% 0.65/0.90 343[4:MRR:334.1,11.0] || -> product1(e_3,e_2,e_4)*.
% 0.65/0.90 357[4:Res:343.0,21.0] || product1(e_3,u,e_4)*+ -> equalish(u,e_2).
% 0.65/0.90 418[5:Spt:312.0,312.3] || product1(e_4,e_1,u)*+ -> equalish(u,e_2).
% 0.65/0.90 446[6:Spt:314.0,314.3] || product1(u,e_1,e_2)*+ -> equalish(u,e_4).
% 0.65/0.90 447[6:Res:172.3,446.0] group_element(u) || -> product1(u,e_1,e_4) product1(u,e_1,e_3)* equalish(e_1,u) equalish(u,e_4).
% 0.65/0.90 640[6:Res:447.2,46.0] group_element(e_3) || -> product1(e_3,e_1,e_4)* equalish(e_1,e_3) equalish(e_3,e_4) equalish(e_1,e_3).
% 0.65/0.90 656[6:Obv:640.2] group_element(e_3) || -> product1(e_3,e_1,e_4)* equalish(e_3,e_4) equalish(e_1,e_3).
% 0.65/0.90 657[6:SSi:656.0,5.0] || -> product1(e_3,e_1,e_4)* equalish(e_3,e_4) equalish(e_1,e_3).
% 0.65/0.90 658[6:MRR:657.1,657.2,15.0,8.0] || -> product1(e_3,e_1,e_4)*.
% 0.65/0.90 668[6:Res:658.0,357.0] || -> equalish(e_1,e_2)*.
% 0.65/0.90 669[6:MRR:668.0,7.0] || -> .
% 0.65/0.90 671[6:Spt:669.0,314.1,314.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.65/0.90 677[6:Res:671.1,150.0] || -> product1(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.65/0.90 680[6:MRR:677.0,677.1,418.0,17.0] || -> .
% 0.65/0.90 683[5:Spt:680.0,312.1,312.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.65/0.90 689[5:Res:683.1,150.0] || -> product1(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.65/0.90 691[5:MRR:689.1,17.0] || -> product1(e_4,e_1,e_4)*.
% 0.65/0.90 693[5:Res:691.0,46.0] || -> equalish(e_1,e_4)*.
% 0.65/0.90 701[5:MRR:693.0,9.0] || -> .
% 0.65/0.90 703[3:Spt:701.0,131.1] || -> product1(e_2,e_1,e_4)*.
% 0.65/0.90 712[3:Res:703.0,132.0] || -> equalish(e_4,e_3)*.
% 0.65/0.90 714[3:MRR:712.0,18.0] || -> .
% 0.65/0.90 718[2:Spt:714.0,129.1] || -> product1(e_2,e_1,e_4)*.
% 0.65/0.90 722[2:Res:718.0,74.2] group_element(e_2) group_element(e_4) || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.65/0.90 726[2:Res:718.0,22.0] || product1(u,e_1,e_4)*+ -> equalish(u,e_2).
% 0.65/0.90 730[2:SSi:722.1,722.0,6.0,4.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.65/0.90 771[3:Spt:187.0,187.2] || product1(u,e_2,e_3)*+ -> equalish(u,e_1).
% 0.65/0.90 831[2:Res:730.3,41.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)* equalish(e_2,e_1).
% 0.65/0.90 833[2:MRR:831.3,10.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)*.
% 0.65/0.90 840[2:Res:833.2,44.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.65/0.90 842[2:MRR:840.2,17.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)*.
% 0.65/0.90 892[2:Res:842.1,74.2] group_element(e_4) group_element(e_3) || -> product1(e_4,e_2,e_4) product1(e_3,e_4,e_4) product1(e_3,e_4,e_3) product1(e_3,e_4,e_2) product2(e_1,e_2,e_4)*.
% 0.65/0.90 897[3:Res:842.1,771.0] || -> product1(e_4,e_2,e_4)* equalish(e_4,e_1).
% 0.65/0.90 899[3:MRR:897.1,16.0] || -> product1(e_4,e_2,e_4)*.
% 0.65/0.90 901[3:Res:899.0,46.0] || -> equalish(e_2,e_4)*.
% 0.65/0.90 909[3:MRR:901.0,12.0] || -> .
% 0.65/0.90 911[3:Spt:909.0,187.1] || -> product1(e_1,e_2,e_4)*.
% 0.65/0.90 912[2:SSi:892.1,892.0,5.0,6.0] || -> product1(e_4,e_2,e_4) product1(e_3,e_4,e_4) product1(e_3,e_4,e_3) product1(e_3,e_4,e_2) product2(e_1,e_2,e_4)*.
% 0.65/0.90 920[4:Spt:842.0] || -> product1(e_4,e_2,e_4)*.
% 0.65/0.90 921[4:Res:920.0,46.0] || -> equalish(e_2,e_4)*.
% 0.65/0.90 929[4:MRR:921.0,12.0] || -> .
% 0.65/0.90 931[4:Spt:929.0,842.0,920.0] || product1(e_4,e_2,e_4)*+ -> .
% 0.65/0.90 932[4:Spt:929.0,842.1] || -> product1(e_4,e_2,e_3)*.
% 0.65/0.90 937[4:MRR:912.0,931.0] || -> product1(e_3,e_4,e_4) product1(e_3,e_4,e_3) product1(e_3,e_4,e_2) product2(e_1,e_2,e_4)*.
% 0.65/0.90 1087[4:Res:937.3,106.0] || -> product1(e_3,e_4,e_4) product1(e_3,e_4,e_3) product1(e_3,e_4,e_2)* equalish(e_4,e_3).
% 0.65/0.90 1088[4:MRR:1087.1,1087.3,46.0,18.0] || -> product1(e_3,e_4,e_4) product1(e_3,e_4,e_2)*.
% 0.65/0.90 1091[4:Res:1088.1,20.0] || product1(e_3,e_4,u)*+ -> product1(e_3,e_4,e_4)* equalish(u,e_2).
% 0.65/0.90 1092[4:Res:1088.1,21.0] || product1(e_3,u,e_2)*+ -> product1(e_3,e_4,e_4)* equalish(u,e_4).
% 0.65/0.90 1112[5:Spt:1091.0,1091.2] || product1(e_3,e_4,u)*+ -> equalish(u,e_2).
% 0.65/0.90 1119[6:Spt:1092.0,1092.2] || product1(e_3,u,e_2)*+ -> equalish(u,e_4).
% 0.65/0.90 1121[6:Res:172.3,1119.0] group_element(e_3) || -> product1(e_3,e_1,e_4) product1(e_3,e_1,e_3)* equalish(e_1,e_3) equalish(e_1,e_4).
% 0.65/0.90 1129[6:SSi:1121.0,5.0] || -> product1(e_3,e_1,e_4) product1(e_3,e_1,e_3)* equalish(e_1,e_3) equalish(e_1,e_4).
% 0.65/0.90 1130[6:MRR:1129.1,1129.2,1129.3,46.0,8.0,9.0] || -> product1(e_3,e_1,e_4)*.
% 0.65/0.90 1140[6:Res:1130.0,726.0] || -> equalish(e_3,e_2)*.
% 0.65/0.90 1142[6:MRR:1140.0,14.0] || -> .
% 0.65/0.90 1151[6:Spt:1142.0,1092.1] || -> product1(e_3,e_4,e_4)*.
% 0.65/0.90 1159[6:Res:1151.0,1112.0] || -> equalish(e_4,e_2)*.
% 0.65/0.90 1161[6:MRR:1159.0,17.0] || -> .
% 0.65/0.90 1163[5:Spt:1161.0,1091.1] || -> product1(e_3,e_4,e_4)*.
% 0.65/0.90 1169[5:Res:1163.0,44.0] || -> equalish(e_3,e_4)*.
% 0.65/0.90 1171[5:MRR:1169.0,15.0] || -> .
% 0.65/0.90 1173[1:Spt:1171.0,103.1] || -> product2(e_1,e_2,e_4)*.
% 0.65/0.90 1174[1:Res:1173.0,25.0] || product2(e_1,e_2,u)*+ -> equalish(u,e_4).
% 0.65/0.90 1178[2:Spt:183.0] || -> product1(e_1,e_2,e_4)*.
% 0.65/0.90 1179[2:Res:1178.0,74.2] group_element(e_1) group_element(e_4) || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2) product2(e_1,e_2,e_1)*.
% 0.65/0.90 1183[2:Res:1178.0,22.0] || product1(u,e_2,e_4)*+ -> equalish(u,e_1).
% 0.65/0.90 1185[2:SSi:1179.1,1179.0,6.0,3.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2) product2(e_1,e_2,e_1)*.
% 0.65/0.90 1186[3:Spt:127.0] || -> product1(e_2,e_1,e_4)*.
% 0.65/0.90 1187[3:Res:1186.0,74.2] group_element(e_2) group_element(e_4) || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.65/0.90 1191[3:Res:1186.0,22.0] || product1(u,e_1,e_4)*+ -> equalish(u,e_2).
% 0.65/0.90 1195[3:SSi:1187.1,1187.0,6.0,4.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.65/0.90 1290[2:Res:1185.3,40.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)* equalish(e_2,e_1).
% 0.65/0.90 1298[2:MRR:1290.3,10.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)*.
% 0.65/0.90 1319[2:Res:1298.2,29.0] || product1(e_1,u,e_4)+ -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product2(e_2,u,e_1)*.
% 0.65/0.90 1320[2:Res:1298.2,20.0] || product1(e_4,e_1,u)*+ -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(u,e_2).
% 0.65/0.90 1329[3:Res:1195.3,41.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)* equalish(e_2,e_1).
% 0.65/0.90 1332[3:MRR:1329.3,10.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)*.
% 0.65/0.90 1339[3:Res:1332.2,44.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.65/0.90 1341[3:MRR:1339.2,17.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)*.
% 0.65/0.90 1345[3:Res:1341.1,20.0] || product1(e_4,e_2,u)*+ -> product1(e_4,e_2,e_4)* equalish(u,e_3).
% 0.65/0.90 1346[3:Res:1341.1,21.0] || product1(e_4,u,e_3)*+ -> product1(e_4,e_2,e_4)* equalish(u,e_2).
% 0.65/0.90 1379[4:Spt:1345.0,1345.2] || product1(e_4,e_2,u)*+ -> equalish(u,e_3).
% 0.65/0.90 1386[5:Spt:1346.0,1346.2] || product1(e_4,u,e_3)*+ -> equalish(u,e_2).
% 0.65/0.90 1512[6:Spt:1320.0,1320.3] || product1(e_4,e_1,u)*+ -> equalish(u,e_2).
% 0.65/0.90 1717[7:Spt:1319.0,1319.3] || product1(e_1,u,e_4)+ -> product2(e_2,u,e_1)*.
% 0.65/0.90 1720[7:Res:1178.0,1717.0] || -> product2(e_2,e_2,e_1)*.
% 0.65/0.90 1743[7:Res:1720.0,41.0] || -> equalish(e_1,e_2)*.
% 0.65/0.90 1747[7:MRR:1743.0,7.0] || -> .
% 0.65/0.90 1751[7:Spt:1747.0,1319.1,1319.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.65/0.90 1758[7:Res:1751.1,1386.0] || -> product1(e_4,e_1,e_4)* equalish(e_1,e_2).
% 0.65/0.90 1760[7:MRR:1758.1,7.0] || -> product1(e_4,e_1,e_4)*.
% 0.65/0.90 1771[7:Res:1760.0,1512.0] || -> equalish(e_4,e_2)*.
% 0.65/0.90 1774[7:MRR:1771.0,17.0] || -> .
% 0.65/0.90 1793[6:Spt:1774.0,1320.1,1320.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.65/0.90 1801[6:Res:1793.1,1386.0] || -> product1(e_4,e_1,e_4)* equalish(e_1,e_2).
% 0.65/0.90 1802[6:MRR:1801.1,7.0] || -> product1(e_4,e_1,e_4)*.
% 0.65/0.90 1811[6:Res:1802.0,1191.0] || -> equalish(e_4,e_2)*.
% 0.65/0.90 1814[6:MRR:1811.0,17.0] || -> .
% 0.65/0.90 1823[5:Spt:1814.0,1346.1] || -> product1(e_4,e_2,e_4)*.
% 0.65/0.90 1833[5:Res:1823.0,1379.0] || -> equalish(e_4,e_3)*.
% 0.65/0.90 1836[5:MRR:1833.0,18.0] || -> .
% 0.65/0.90 1841[4:Spt:1836.0,1345.1] || -> product1(e_4,e_2,e_4)*.
% 0.65/0.90 1849[4:Res:1841.0,1183.0] || -> equalish(e_4,e_1)*.
% 0.65/0.90 1852[4:MRR:1849.0,16.0] || -> .
% 0.65/0.90 1857[3:Spt:1852.0,127.0,1186.0] || product1(e_2,e_1,e_4)*+ -> .
% 0.65/0.90 1858[3:Spt:1852.0,127.1] || -> product1(e_2,e_1,e_3)*.
% 0.65/0.90 1859[3:MRR:131.1,1857.0] || product1(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.65/0.90 1952[4:Spt:1298.0] || -> product1(e_4,e_1,e_4)*.
% 0.65/0.90 1953[4:Res:1952.0,46.0] || -> equalish(e_1,e_4)*.
% 0.65/0.90 1961[4:MRR:1953.0,9.0] || -> .
% 0.65/0.90 1964[4:Spt:1961.0,1298.0,1952.0] || product1(e_4,e_1,e_4)*+ -> .
% 0.65/0.90 1965[4:Spt:1961.0,1298.1,1298.2] || -> product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)*.
% 0.65/0.90 1969[4:MRR:1319.1,1964.0] || product1(e_1,u,e_4) -> product1(e_4,e_1,e_3) product2(e_2,u,e_1)*.
% 0.65/0.90 1972[5:Spt:1965.0] || -> product1(e_4,e_1,e_3)*.
% 0.65/0.90 1978[5:Res:1972.0,1859.0] || -> equalish(e_4,e_2)*.
% 0.65/0.90 1980[5:MRR:1978.0,17.0] || -> .
% 0.65/0.90 1989[5:Spt:1980.0,1965.0,1972.0] || product1(e_4,e_1,e_3)*+ -> .
% 0.65/0.90 1990[5:Spt:1980.0,1965.1] || -> product1(e_4,e_1,e_2)*.
% 0.65/0.90 1994[5:MRR:1969.1,1989.0] || product1(e_1,u,e_4)+ -> product2(e_2,u,e_1)*.
% 0.65/0.90 2080[5:Res:1178.0,1994.0] || -> product2(e_2,e_2,e_1)*.
% 0.65/0.92 2084[5:Res:2080.0,41.0] || -> equalish(e_1,e_2)*.
% 0.65/0.92 2088[5:MRR:2084.0,7.0] || -> .
% 0.65/0.92 2092[2:Spt:2088.0,183.0,1178.0] || product1(e_1,e_2,e_4)*+ -> .
% 0.65/0.92 2093[2:Spt:2088.0,183.1] || -> product1(e_1,e_2,e_3)*.
% 0.65/0.92 2096[2:MRR:187.1,2092.0] || product1(u,e_2,e_3)*+ -> equalish(u,e_1).
% 0.65/0.92 2108[3:Spt:127.0] || -> product1(e_2,e_1,e_4)*.
% 0.65/0.92 2109[3:Res:2108.0,74.2] group_element(e_2) group_element(e_4) || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.65/0.92 2118[3:SSi:2109.1,2109.0,6.0,4.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.65/0.92 2247[3:Res:2118.3,41.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)* equalish(e_2,e_1).
% 0.65/0.92 2254[3:MRR:2247.3,10.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)*.
% 0.65/0.92 2281[3:Res:2254.2,44.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.65/0.92 2285[3:MRR:2281.2,17.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)*.
% 0.65/0.92 2292[3:Res:2285.1,2096.0] || -> product1(e_4,e_2,e_4)* equalish(e_4,e_1).
% 0.65/0.92 2294[3:MRR:2292.1,16.0] || -> product1(e_4,e_2,e_4)*.
% 0.65/0.92 2296[3:Res:2294.0,46.0] || -> equalish(e_2,e_4)*.
% 0.65/0.92 2304[3:MRR:2296.0,12.0] || -> .
% 0.65/0.92 2308[3:Spt:2304.0,127.0,2108.0] || product1(e_2,e_1,e_4)*+ -> .
% 0.65/0.92 2309[3:Spt:2304.0,127.1] || -> product1(e_2,e_1,e_3)*.
% 0.65/0.92 2310[3:MRR:131.1,2308.0] || product1(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.65/0.92 2316[3:Res:2309.0,74.2] group_element(e_2) group_element(e_3) || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.65/0.92 2323[3:SSi:2316.1,2316.0,5.0,4.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2) product2(e_1,e_1,e_2)*.
% 0.65/0.92 2425[3:Res:2323.3,41.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2)* equalish(e_2,e_1).
% 0.65/0.92 2432[3:MRR:2425.3,10.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2)*.
% 0.65/0.92 2441[3:Res:2432.2,44.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)* equalish(e_3,e_2).
% 0.65/0.92 2445[3:MRR:2441.2,14.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)*.
% 0.65/0.92 2447[3:Res:2445.1,46.0] || -> product1(e_3,e_2,e_4)* equalish(e_2,e_3).
% 0.65/0.92 2456[3:MRR:2447.1,11.0] || -> product1(e_3,e_2,e_4)*.
% 0.65/0.92 2459[3:Res:2456.0,74.2] group_element(e_3) group_element(e_4) || -> product1(e_4,e_3,e_4) product1(e_4,e_3,e_3) product1(e_4,e_3,e_2) product2(e_1,e_2,e_3)*.
% 0.65/0.92 2465[3:SSi:2459.1,2459.0,6.0,5.0] || -> product1(e_4,e_3,e_4) product1(e_4,e_3,e_3) product1(e_4,e_3,e_2) product2(e_1,e_2,e_3)*.
% 0.65/0.92 2642[3:Res:2465.3,1174.0] || -> product1(e_4,e_3,e_4) product1(e_4,e_3,e_3) product1(e_4,e_3,e_2)* equalish(e_3,e_4).
% 0.65/0.92 2643[3:MRR:2642.0,2642.3,46.0,15.0] || -> product1(e_4,e_3,e_3) product1(e_4,e_3,e_2)*.
% 0.65/0.92 2649[3:Res:2643.1,124.1] group_element(e_4) || -> product1(e_4,e_3,e_3) product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(e_4,e_1) equalish(e_3,e_1).
% 0.65/0.92 2650[3:Res:2643.1,179.1] group_element(e_3) || -> product1(e_4,e_3,e_3) product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)* equalish(e_3,e_1) equalish(e_4,e_1).
% 0.65/0.92 2652[3:SSi:2650.0,5.0] || -> product1(e_4,e_3,e_3) product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)* equalish(e_3,e_1) equalish(e_4,e_1).
% 0.65/0.92 2653[3:MRR:2652.3,2652.4,13.0,16.0] || -> product1(e_4,e_3,e_3) product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)*.
% 0.65/0.92 2654[3:SSi:2649.0,6.0] || -> product1(e_4,e_3,e_3) product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(e_4,e_1) equalish(e_3,e_1).
% 0.65/0.92 2655[3:MRR:2654.3,2654.4,16.0,13.0] || -> product1(e_4,e_3,e_3) product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.65/0.92 2658[4:Spt:2653.0] || -> product1(e_4,e_3,e_3)*.
% 0.65/0.92 2664[4:Res:2658.0,44.0] || -> equalish(e_4,e_3)*.
% 0.65/0.92 2666[4:MRR:2664.0,18.0] || -> .
% 0.65/0.92 2668[4:Spt:2666.0,2653.0,2658.0] || product1(e_4,e_3,e_3)*+ -> .
% 0.65/0.92 2669[4:Spt:2666.0,2653.1,2653.2] || -> product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)*.
% 0.65/0.92 2674[4:MRR:2655.0,2668.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.65/0.92 2709[4:Res:2674.1,2310.0] || -> product1(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.65/0.92 2712[4:MRR:2709.1,17.0] || -> product1(e_4,e_1,e_4)*.
% 0.65/0.92 2715[4:Res:2712.0,46.0] || -> equalish(e_1,e_4)*.
% 0.65/0.92 2724[4:MRR:2715.0,9.0] || -> .
% 0.65/0.92 % SZS output end Refutation
% 0.65/0.92 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_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 product1_total_function1 product1_total_function2 product1_right_cancellation product1_left_cancellation product1_idempotence product2_total_function1 product2_total_function2 product2_right_cancellation product2_left_cancellation product2_idempotence qg2a
% 0.65/0.92
%------------------------------------------------------------------------------