TSTP Solution File: GRP124-7.004 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP124-7.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:45:32 EDT 2022
% Result : Unsatisfiable 0.75s 0.97s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP124-7.004 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 23:01:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.75/0.97
% 0.75/0.97 SPASS V 3.9
% 0.75/0.97 SPASS beiseite: Proof found.
% 0.75/0.97 % SZS status Theorem
% 0.75/0.97 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.75/0.97 SPASS derived 2093 clauses, backtracked 224 clauses, performed 37 splits and kept 1087 clauses.
% 0.75/0.97 SPASS allocated 77866 KBytes.
% 0.75/0.97 SPASS spent 0:00:00.62 on the problem.
% 0.75/0.97 0:00:00.04 for the input.
% 0.75/0.97 0:00:00.00 for the FLOTTER CNF translation.
% 0.75/0.97 0:00:00.04 for inferences.
% 0.75/0.97 0:00:00.01 for the backtracking.
% 0.75/0.97 0:00:00.51 for the reduction.
% 0.75/0.97
% 0.75/0.97
% 0.75/0.97 Here is a proof with depth 14, length 251 :
% 0.75/0.97 % SZS output start Refutation
% 0.75/0.97 11[0:Inp] || -> group_element(e_1)*.
% 0.75/0.97 12[0:Inp] || -> group_element(e_2)*.
% 0.75/0.97 13[0:Inp] || -> group_element(e_3)*.
% 0.75/0.97 14[0:Inp] || -> group_element(e_4)*.
% 0.75/0.97 15[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.75/0.97 16[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.75/0.97 17[0:Inp] || equalish(e_1,e_4)*+ -> .
% 0.75/0.97 18[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.75/0.97 19[0:Inp] || equalish(e_2,e_3)*+ -> .
% 0.75/0.97 20[0:Inp] || equalish(e_2,e_4)*+ -> .
% 0.75/0.97 21[0:Inp] || equalish(e_3,e_1)*+ -> .
% 0.75/0.97 22[0:Inp] || equalish(e_3,e_2)*+ -> .
% 0.75/0.97 23[0:Inp] || equalish(e_3,e_4)*+ -> .
% 0.75/0.97 24[0:Inp] || equalish(e_4,e_1)*+ -> .
% 0.75/0.97 25[0:Inp] || equalish(e_4,e_2)*+ -> .
% 0.75/0.97 26[0:Inp] || equalish(e_4,e_3)*+ -> .
% 0.75/0.97 27[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)*.
% 0.75/0.97 28[0:Inp] || product1(u,v,w)*+ product1(u,v,x)* -> equalish(x,w)*.
% 0.75/0.97 29[0:Inp] || product1(u,v,w)*+ product1(u,x,w)* -> equalish(x,v)*.
% 0.75/0.97 30[0:Inp] || product1(u,v,w)*+ product1(x,v,w)* -> equalish(x,u)*.
% 0.75/0.97 31[0:Inp] || -> product1(u,u,u)*.
% 0.75/0.97 32[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)*.
% 0.75/0.97 33[0:Inp] || product2(u,v,w)*+ product2(u,v,x)* -> equalish(x,w)*.
% 0.75/0.97 34[0:Inp] || product2(u,v,w)*+ product2(u,x,w)* -> equalish(x,v)*.
% 0.75/0.97 35[0:Inp] || product2(u,v,w)*+ product2(x,v,w)* -> equalish(x,u)*.
% 0.75/0.97 36[0:Inp] || -> product2(u,u,u)*.
% 0.75/0.97 37[0:Inp] || product1(u,v,w)*+ product1(v,x,u)* -> product2(w,x,v)*.
% 0.75/0.97 46[0:Res:36.0,35.0] || product2(u,v,v)*+ -> equalish(u,v).
% 0.75/0.97 48[0:Res:36.0,34.0] || product2(u,v,u)*+ -> equalish(v,u).
% 0.75/0.97 49[0:Res:36.0,33.0] || product2(u,u,v)*+ -> equalish(v,u).
% 0.75/0.97 52[0:Res:31.0,30.0] || product1(u,v,v)*+ -> equalish(u,v).
% 0.75/0.97 54[0:Res:31.0,29.0] || product1(u,v,u)*+ -> equalish(v,u).
% 0.75/0.97 59[0:Res:32.5,48.0] 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).
% 0.75/0.97 67[0:SSi:59.1,11.0] 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).
% 0.75/0.97 84[0:Res:27.5,54.0] 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).
% 0.75/0.97 88[0:Res:27.5,37.0] 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)*.
% 0.75/0.97 91[0:Res:27.5,30.0] 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)*.
% 0.75/0.97 92[0:Res:27.5,52.0] 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).
% 0.75/0.97 93[0:SSi:92.0,11.0] 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).
% 0.75/0.97 95[0:SSi:84.1,11.0] 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).
% 0.75/0.97 103[0:Res:67.3,46.0] 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).
% 0.75/0.97 105[0:SSi:103.0,12.0] || -> product2(e_1,e_2,e_4) product2(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.75/0.97 106[0:MRR:105.2,105.3,18.0,15.0] || -> product2(e_1,e_2,e_4) product2(e_1,e_2,e_3)*.
% 0.75/0.97 107[0:Res:106.1,33.0] || product2(e_1,e_2,u)*+ -> product2(e_1,e_2,e_4)* equalish(u,e_3).
% 0.75/0.97 110[1:Spt:107.0,107.2] || product2(e_1,e_2,u)*+ -> equalish(u,e_3).
% 0.75/0.97 122[0:Res:93.3,54.0] 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).
% 0.75/0.97 128[0:Res:93.3,29.0] 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).
% 0.75/0.97 130[0:SSi:122.0,12.0] || -> product1(e_2,e_1,e_4) product1(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.75/0.97 131[0:MRR:130.2,130.3,18.0,15.0] || -> product1(e_2,e_1,e_4) product1(e_2,e_1,e_3)*.
% 0.75/0.97 132[0:Res:131.1,37.0] || product1(e_1,u,e_2)+ -> product1(e_2,e_1,e_4) product2(e_3,u,e_1)*.
% 0.75/0.97 133[0:Res:131.1,28.0] || product1(e_2,e_1,u)*+ -> product1(e_2,e_1,e_4)* equalish(u,e_3).
% 0.75/0.97 135[0:Res:131.1,30.0] || product1(u,e_1,e_3)*+ -> product1(e_2,e_1,e_4)* equalish(u,e_2).
% 0.75/0.97 140[2:Spt:133.0,133.2] || product1(e_2,e_1,u)*+ -> equalish(u,e_3).
% 0.75/0.97 146[3:Spt:135.0,135.2] || product1(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.75/0.97 148[4:Spt:132.1] || -> product1(e_2,e_1,e_4)*.
% 0.75/0.97 153[4:Res:148.0,140.0] || -> equalish(e_4,e_3)*.
% 0.75/0.97 154[4:MRR:153.0,26.0] || -> .
% 0.75/0.97 155[4:Spt:154.0,132.1,148.0] || product1(e_2,e_1,e_4)*+ -> .
% 0.75/0.97 156[4:Spt:154.0,132.0,132.2] || product1(e_1,u,e_2)+ -> product2(e_3,u,e_1)*.
% 0.75/0.97 157[4:MRR:131.0,155.0] || -> product1(e_2,e_1,e_3)*.
% 0.75/0.97 171[0:Res:95.3,30.0] 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).
% 0.75/0.97 172[0:Res:95.3,52.0] 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).
% 0.75/0.97 173[4:Res:95.3,156.0] 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)*.
% 0.75/0.97 174[0:SSi:172.0,12.0] || -> product1(e_1,e_2,e_4) product1(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.75/0.97 175[0:MRR:174.2,174.3,18.0,15.0] || -> product1(e_1,e_2,e_4) product1(e_1,e_2,e_3)*.
% 0.75/0.97 179[0:Res:175.1,30.0] || product1(u,e_2,e_3)*+ -> product1(e_1,e_2,e_4)* equalish(u,e_1).
% 0.75/0.97 211[0:Res:31.0,91.2] 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).
% 0.75/0.97 213[0:SSi:211.0,11.0] 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).
% 0.75/0.97 228[4:Res:173.4,49.0] 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).
% 0.75/0.97 232[4:SSi:228.0,13.0] || -> product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)* equalish(e_3,e_1) equalish(e_1,e_3).
% 0.75/0.97 233[4:MRR:232.1,232.2,232.3,52.0,21.0,16.0] || -> product1(e_1,e_3,e_4)*.
% 0.75/0.97 326[4:Res:157.0,88.2] 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)*.
% 0.75/0.97 330[4:Res:233.0,88.2] 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)*.
% 0.75/0.97 331[4:SSi:330.1,330.0,14.0,11.0] || -> 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)*.
% 0.75/0.97 332[4:SSi:326.1,326.0,13.0,12.0] || -> 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)*.
% 0.75/0.97 342[4:Res:331.3,48.0] || -> 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).
% 0.75/0.97 349[4:MRR:342.3,21.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)*.
% 0.75/0.97 352[4:Res:349.2,28.0] || product1(e_4,e_1,u)*+ -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(u,e_2).
% 0.75/0.97 354[4:Res:349.2,30.0] || product1(u,e_1,e_2)*+ -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(u,e_4).
% 0.75/0.97 361[4:Res:332.3,49.0] || -> 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).
% 0.75/0.97 363[4:MRR:361.3,18.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2)*.
% 0.75/0.97 370[4:Res:363.2,52.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)* equalish(e_3,e_2).
% 0.75/0.97 372[4:MRR:370.2,22.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)*.
% 0.75/0.97 390[4:Res:372.1,54.0] || -> product1(e_3,e_2,e_4)* equalish(e_2,e_3).
% 0.75/0.97 399[4:MRR:390.1,19.0] || -> product1(e_3,e_2,e_4)*.
% 0.75/0.97 405[4:Res:399.0,29.0] || product1(e_3,u,e_4)*+ -> equalish(u,e_2).
% 0.75/0.97 466[5:Spt:352.0,352.3] || product1(e_4,e_1,u)*+ -> equalish(u,e_2).
% 0.75/0.97 491[6:Spt:354.0,354.3] || product1(u,e_1,e_2)*+ -> equalish(u,e_4).
% 0.75/0.97 492[6:Res:213.3,491.0] group_element(u) || -> product1(u,e_1,e_4) product1(u,e_1,e_3)* equalish(e_1,u) equalish(u,e_4).
% 0.75/0.97 729[6:Res:492.2,54.0] 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).
% 0.75/0.97 745[6:Obv:729.2] group_element(e_3) || -> product1(e_3,e_1,e_4)* equalish(e_3,e_4) equalish(e_1,e_3).
% 0.75/0.97 746[6:SSi:745.0,13.0] || -> product1(e_3,e_1,e_4)* equalish(e_3,e_4) equalish(e_1,e_3).
% 0.75/0.97 747[6:MRR:746.1,746.2,23.0,16.0] || -> product1(e_3,e_1,e_4)*.
% 0.75/0.97 819[6:Res:747.0,405.0] || -> equalish(e_1,e_2)*.
% 0.75/0.97 820[6:MRR:819.0,15.0] || -> .
% 0.75/0.97 822[6:Spt:820.0,354.1,354.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.75/0.97 828[6:Res:822.1,146.0] || -> product1(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.75/0.97 831[6:MRR:828.0,828.1,466.0,25.0] || -> .
% 0.75/0.97 834[5:Spt:831.0,352.1,352.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.75/0.97 840[5:Res:834.1,146.0] || -> product1(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.75/0.97 842[5:MRR:840.1,25.0] || -> product1(e_4,e_1,e_4)*.
% 0.75/0.97 844[5:Res:842.0,54.0] || -> equalish(e_1,e_4)*.
% 0.75/0.97 852[5:MRR:844.0,17.0] || -> .
% 0.75/0.97 854[3:Spt:852.0,135.1] || -> product1(e_2,e_1,e_4)*.
% 0.75/0.97 864[3:Res:854.0,140.0] || -> equalish(e_4,e_3)*.
% 0.75/0.97 865[3:MRR:864.0,26.0] || -> .
% 0.75/0.97 869[2:Spt:865.0,133.1] || -> product1(e_2,e_1,e_4)*.
% 0.75/0.97 873[2:Res:869.0,88.2] 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)*.
% 0.75/0.97 877[2:Res:869.0,30.0] || product1(u,e_1,e_4)*+ -> equalish(u,e_2).
% 0.75/0.97 881[2:SSi:873.1,873.0,14.0,12.0] || -> 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)*.
% 0.75/0.97 946[3:Spt:179.0,179.2] || product1(u,e_2,e_3)*+ -> equalish(u,e_1).
% 0.75/0.97 979[2:Res:881.3,49.0] || -> 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).
% 0.75/0.97 981[2:MRR:979.3,18.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)*.
% 0.75/0.97 988[2:Res:981.2,52.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.75/0.97 990[2:MRR:988.2,25.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)*.
% 0.75/0.97 992[2:Res:990.1,88.2] 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)*.
% 0.75/0.97 997[3:Res:990.1,946.0] || -> product1(e_4,e_2,e_4)* equalish(e_4,e_1).
% 0.75/0.97 999[3:MRR:997.1,24.0] || -> product1(e_4,e_2,e_4)*.
% 0.75/0.97 1015[3:Res:999.0,54.0] || -> equalish(e_2,e_4)*.
% 0.75/0.97 1023[3:MRR:1015.0,20.0] || -> .
% 0.75/0.97 1025[3:Spt:1023.0,179.1] || -> product1(e_1,e_2,e_4)*.
% 0.75/0.97 1026[2:SSi:992.1,992.0,13.0,14.0] || -> 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)*.
% 0.75/0.97 1034[4:Spt:990.0] || -> product1(e_4,e_2,e_4)*.
% 0.75/0.97 1035[4:Res:1034.0,54.0] || -> equalish(e_2,e_4)*.
% 0.75/0.97 1043[4:MRR:1035.0,20.0] || -> .
% 0.75/0.97 1045[4:Spt:1043.0,990.0,1034.0] || product1(e_4,e_2,e_4)*+ -> .
% 0.75/0.97 1046[4:Spt:1043.0,990.1] || -> product1(e_4,e_2,e_3)*.
% 0.75/0.97 1051[4:MRR:1026.0,1045.0] || -> 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)*.
% 0.75/0.97 1215[4:Res:1051.3,110.0] || -> 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).
% 0.75/0.97 1216[4:MRR:1215.1,1215.3,54.0,26.0] || -> product1(e_3,e_4,e_4) product1(e_3,e_4,e_2)*.
% 0.75/0.97 1219[4:Res:1216.1,28.0] || product1(e_3,e_4,u)*+ -> product1(e_3,e_4,e_4)* equalish(u,e_2).
% 0.75/0.97 1220[4:Res:1216.1,29.0] || product1(e_3,u,e_2)*+ -> product1(e_3,e_4,e_4)* equalish(u,e_4).
% 0.75/0.97 1225[5:Spt:1219.0,1219.2] || product1(e_3,e_4,u)*+ -> equalish(u,e_2).
% 0.75/0.97 1252[6:Spt:1220.0,1220.2] || product1(e_3,u,e_2)*+ -> equalish(u,e_4).
% 0.75/0.97 1254[6:Res:213.3,1252.0] 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).
% 0.75/0.97 1262[6:SSi:1254.0,13.0] || -> product1(e_3,e_1,e_4) product1(e_3,e_1,e_3)* equalish(e_1,e_3) equalish(e_1,e_4).
% 0.75/0.97 1263[6:MRR:1262.1,1262.2,1262.3,54.0,16.0,17.0] || -> product1(e_3,e_1,e_4)*.
% 0.75/0.97 1273[6:Res:1263.0,877.0] || -> equalish(e_3,e_2)*.
% 0.75/0.97 1275[6:MRR:1273.0,22.0] || -> .
% 0.75/0.97 1285[6:Spt:1275.0,1220.1] || -> product1(e_3,e_4,e_4)*.
% 0.75/0.97 1293[6:Res:1285.0,1225.0] || -> equalish(e_4,e_2)*.
% 0.75/0.97 1295[6:MRR:1293.0,25.0] || -> .
% 0.75/0.97 1297[5:Spt:1295.0,1219.1] || -> product1(e_3,e_4,e_4)*.
% 0.75/0.97 1303[5:Res:1297.0,52.0] || -> equalish(e_3,e_4)*.
% 0.75/0.97 1305[5:MRR:1303.0,23.0] || -> .
% 0.75/0.97 1307[1:Spt:1305.0,107.1] || -> product2(e_1,e_2,e_4)*.
% 0.75/0.97 1308[1:Res:1307.0,33.0] || product2(e_1,e_2,u)*+ -> equalish(u,e_4).
% 0.75/0.97 1312[2:Spt:175.0] || -> product1(e_1,e_2,e_4)*.
% 0.75/0.97 1313[2:Res:1312.0,88.2] 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)*.
% 0.75/0.97 1317[2:Res:1312.0,30.0] || product1(u,e_2,e_4)*+ -> equalish(u,e_1).
% 0.75/0.97 1319[2:SSi:1313.1,1313.0,14.0,11.0] || -> 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)*.
% 0.75/0.97 1320[3:Spt:131.0] || -> product1(e_2,e_1,e_4)*.
% 0.75/0.97 1321[3:Res:1320.0,88.2] 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)*.
% 0.75/0.97 1325[3:Res:1320.0,30.0] || product1(u,e_1,e_4)*+ -> equalish(u,e_2).
% 0.75/0.97 1329[3:SSi:1321.1,1321.0,14.0,12.0] || -> 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)*.
% 0.75/0.97 1478[2:Res:1319.3,48.0] || -> 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).
% 0.75/0.97 1486[2:MRR:1478.3,18.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)*.
% 0.75/0.97 1519[2:Res:1486.2,37.0] || 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)*.
% 0.75/0.97 1520[2:Res:1486.2,28.0] || product1(e_4,e_1,u)*+ -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)* equalish(u,e_2).
% 0.75/0.97 1529[3:Res:1329.3,49.0] || -> 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).
% 0.75/0.97 1535[3:MRR:1529.3,18.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)*.
% 0.75/0.97 1544[3:Res:1535.2,52.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.75/0.97 1546[3:MRR:1544.2,25.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)*.
% 0.75/0.97 1550[3:Res:1546.1,28.0] || product1(e_4,e_2,u)*+ -> product1(e_4,e_2,e_4)* equalish(u,e_3).
% 0.75/0.97 1551[3:Res:1546.1,29.0] || product1(e_4,u,e_3)*+ -> product1(e_4,e_2,e_4)* equalish(u,e_2).
% 0.75/0.97 1575[4:Spt:1550.0,1550.2] || product1(e_4,e_2,u)*+ -> equalish(u,e_3).
% 0.75/0.97 1582[5:Spt:1551.0,1551.2] || product1(e_4,u,e_3)*+ -> equalish(u,e_2).
% 0.75/0.97 1696[6:Spt:1520.0,1520.3] || product1(e_4,e_1,u)*+ -> equalish(u,e_2).
% 0.75/0.97 1892[7:Spt:1519.0,1519.3] || product1(e_1,u,e_4)+ -> product2(e_2,u,e_1)*.
% 0.75/0.97 1895[7:Res:1312.0,1892.0] || -> product2(e_2,e_2,e_1)*.
% 0.75/0.97 1899[7:Res:1895.0,49.0] || -> equalish(e_1,e_2)*.
% 0.75/0.97 1903[7:MRR:1899.0,15.0] || -> .
% 0.75/0.97 1907[7:Spt:1903.0,1519.1,1519.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.75/0.97 1915[7:Res:1907.1,1696.0] || -> product1(e_4,e_1,e_4)* equalish(e_3,e_2).
% 0.75/0.97 1917[7:MRR:1915.1,22.0] || -> product1(e_4,e_1,e_4)*.
% 0.75/0.97 1930[7:Res:1917.0,1696.0] || -> equalish(e_4,e_2)*.
% 0.75/0.97 1933[7:MRR:1930.0,25.0] || -> .
% 0.75/0.97 1952[6:Spt:1933.0,1520.1,1520.2] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.75/0.97 1961[6:Res:1952.1,1582.0] || -> product1(e_4,e_1,e_4)* equalish(e_1,e_2).
% 0.75/0.97 1962[6:MRR:1961.1,15.0] || -> product1(e_4,e_1,e_4)*.
% 0.75/0.97 1998[6:Res:1962.0,1325.0] || -> equalish(e_4,e_2)*.
% 0.75/0.97 2002[6:MRR:1998.0,25.0] || -> .
% 0.75/0.97 2011[5:Spt:2002.0,1551.1] || -> product1(e_4,e_2,e_4)*.
% 0.75/0.97 2021[5:Res:2011.0,1575.0] || -> equalish(e_4,e_3)*.
% 0.75/0.97 2024[5:MRR:2021.0,26.0] || -> .
% 0.75/0.97 2029[4:Spt:2024.0,1550.1] || -> product1(e_4,e_2,e_4)*.
% 0.75/0.97 2037[4:Res:2029.0,1317.0] || -> equalish(e_4,e_1)*.
% 0.75/0.97 2040[4:MRR:2037.0,24.0] || -> .
% 0.75/0.97 2045[3:Spt:2040.0,131.0,1320.0] || product1(e_2,e_1,e_4)*+ -> .
% 0.75/0.97 2046[3:Spt:2040.0,131.1] || -> product1(e_2,e_1,e_3)*.
% 0.75/0.97 2047[3:MRR:135.1,2045.0] || product1(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.75/0.97 2123[4:Spt:1486.0] || -> product1(e_4,e_1,e_4)*.
% 0.75/0.97 2124[4:Res:2123.0,54.0] || -> equalish(e_1,e_4)*.
% 0.75/0.97 2133[4:MRR:2124.0,17.0] || -> .
% 0.75/0.97 2136[4:Spt:2133.0,1486.0,2123.0] || product1(e_4,e_1,e_4)*+ -> .
% 0.75/0.97 2137[4:Spt:2133.0,1486.1,1486.2] || -> product1(e_4,e_1,e_3) product1(e_4,e_1,e_2)*.
% 0.75/0.97 2141[4:MRR:1519.1,2136.0] || product1(e_1,u,e_4) -> product1(e_4,e_1,e_3) product2(e_2,u,e_1)*.
% 0.75/0.97 2144[5:Spt:2137.0] || -> product1(e_4,e_1,e_3)*.
% 0.75/0.97 2150[5:Res:2144.0,2047.0] || -> equalish(e_4,e_2)*.
% 0.75/0.97 2153[5:MRR:2150.0,25.0] || -> .
% 0.75/0.97 2162[5:Spt:2153.0,2137.0,2144.0] || product1(e_4,e_1,e_3)*+ -> .
% 0.75/0.97 2163[5:Spt:2153.0,2137.1] || -> product1(e_4,e_1,e_2)*.
% 0.75/0.97 2167[5:MRR:2141.1,2162.0] || product1(e_1,u,e_4)+ -> product2(e_2,u,e_1)*.
% 0.75/1.00 2220[5:Res:1312.0,2167.0] || -> product2(e_2,e_2,e_1)*.
% 0.75/1.00 2242[5:Res:2220.0,49.0] || -> equalish(e_1,e_2)*.
% 0.75/1.00 2246[5:MRR:2242.0,15.0] || -> .
% 0.75/1.00 2250[2:Spt:2246.0,175.0,1312.0] || product1(e_1,e_2,e_4)*+ -> .
% 0.75/1.00 2251[2:Spt:2246.0,175.1] || -> product1(e_1,e_2,e_3)*.
% 0.75/1.00 2254[2:MRR:179.1,2250.0] || product1(u,e_2,e_3)*+ -> equalish(u,e_1).
% 0.75/1.00 2266[3:Spt:131.0] || -> product1(e_2,e_1,e_4)*.
% 0.75/1.00 2267[3:Res:2266.0,88.2] 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)*.
% 0.75/1.00 2276[3:SSi:2267.1,2267.0,14.0,12.0] || -> 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)*.
% 0.75/1.00 2440[3:Res:2276.3,49.0] || -> 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).
% 0.75/1.00 2448[3:MRR:2440.3,18.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3) product1(e_4,e_2,e_2)*.
% 0.75/1.00 2458[3:Res:2448.2,52.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)* equalish(e_4,e_2).
% 0.75/1.00 2462[3:MRR:2458.2,25.0] || -> product1(e_4,e_2,e_4) product1(e_4,e_2,e_3)*.
% 0.75/1.00 2469[3:Res:2462.1,2254.0] || -> product1(e_4,e_2,e_4)* equalish(e_4,e_1).
% 0.75/1.00 2471[3:MRR:2469.1,24.0] || -> product1(e_4,e_2,e_4)*.
% 0.75/1.00 2504[3:Res:2471.0,54.0] || -> equalish(e_2,e_4)*.
% 0.75/1.00 2512[3:MRR:2504.0,20.0] || -> .
% 0.75/1.00 2516[3:Spt:2512.0,131.0,2266.0] || product1(e_2,e_1,e_4)*+ -> .
% 0.75/1.00 2517[3:Spt:2512.0,131.1] || -> product1(e_2,e_1,e_3)*.
% 0.75/1.00 2518[3:MRR:135.1,2516.0] || product1(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.75/1.00 2524[3:Res:2517.0,88.2] 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)*.
% 0.75/1.00 2531[3:SSi:2524.1,2524.0,13.0,12.0] || -> 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)*.
% 0.75/1.00 2601[3:Res:2531.3,49.0] || -> 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).
% 0.75/1.00 2610[3:MRR:2601.3,18.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3) product1(e_3,e_2,e_2)*.
% 0.75/1.00 2621[3:Res:2610.2,52.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)* equalish(e_3,e_2).
% 0.75/1.00 2625[3:MRR:2621.2,22.0] || -> product1(e_3,e_2,e_4) product1(e_3,e_2,e_3)*.
% 0.75/1.00 2672[3:Res:2625.1,54.0] || -> product1(e_3,e_2,e_4)* equalish(e_2,e_3).
% 0.75/1.00 2681[3:MRR:2672.1,19.0] || -> product1(e_3,e_2,e_4)*.
% 0.75/1.00 2684[3:Res:2681.0,88.2] 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)*.
% 0.75/1.00 2690[3:SSi:2684.1,2684.0,14.0,13.0] || -> 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)*.
% 0.75/1.00 2821[3:Res:2690.3,1308.0] || -> 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).
% 0.75/1.00 2827[3:MRR:2821.0,2821.3,54.0,23.0] || -> product1(e_4,e_3,e_3) product1(e_4,e_3,e_2)*.
% 0.75/1.00 2833[3:Res:2827.1,128.1] 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).
% 0.75/1.00 2834[3:Res:2827.1,171.1] 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).
% 0.75/1.00 2836[3:SSi:2834.0,13.0] || -> 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).
% 0.75/1.00 2837[3:MRR:2836.3,2836.4,21.0,24.0] || -> product1(e_4,e_3,e_3) product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)*.
% 0.75/1.00 2838[3:SSi:2833.0,14.0] || -> 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).
% 0.75/1.00 2839[3:MRR:2838.3,2838.4,24.0,21.0] || -> product1(e_4,e_3,e_3) product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.75/1.00 2881[4:Spt:2837.0] || -> product1(e_4,e_3,e_3)*.
% 0.75/1.00 2887[4:Res:2881.0,52.0] || -> equalish(e_4,e_3)*.
% 0.75/1.00 2889[4:MRR:2887.0,26.0] || -> .
% 0.75/1.00 2891[4:Spt:2889.0,2837.0,2881.0] || product1(e_4,e_3,e_3)*+ -> .
% 0.75/1.00 2892[4:Spt:2889.0,2837.1,2837.2] || -> product1(e_1,e_3,e_4) product1(e_1,e_3,e_3)*.
% 0.75/1.00 2897[4:MRR:2839.0,2891.0] || -> product1(e_4,e_1,e_4) product1(e_4,e_1,e_3)*.
% 0.75/1.00 2955[4:Res:2897.1,2518.0] || -> product1(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.75/1.00 2958[4:MRR:2955.1,25.0] || -> product1(e_4,e_1,e_4)*.
% 0.75/1.00 2961[4:Res:2958.0,54.0] || -> equalish(e_1,e_4)*.
% 0.75/1.00 2970[4:MRR:2961.0,17.0] || -> .
% 0.75/1.00 % SZS output end Refutation
% 0.75/1.00 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
% 0.75/1.00
%------------------------------------------------------------------------------