TSTP Solution File: GRP132-2.002 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP132-2.002 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:45:49 EDT 2022
% Result : Unsatisfiable 0.94s 1.15s
% Output : Refutation 1.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP132-2.002 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n016.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 20:02:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.94/1.15
% 0.94/1.15 SPASS V 3.9
% 0.94/1.15 SPASS beiseite: Proof found.
% 0.94/1.15 % SZS status Theorem
% 0.94/1.15 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.94/1.15 SPASS derived 2170 clauses, backtracked 603 clauses, performed 20 splits and kept 1400 clauses.
% 0.94/1.15 SPASS allocated 78461 KBytes.
% 0.94/1.15 SPASS spent 0:00:00.80 on the problem.
% 0.94/1.15 0:00:00.03 for the input.
% 0.94/1.15 0:00:00.00 for the FLOTTER CNF translation.
% 0.94/1.15 0:00:00.03 for inferences.
% 0.94/1.15 0:00:00.01 for the backtracking.
% 0.94/1.15 0:00:00.70 for the reduction.
% 0.94/1.15
% 0.94/1.15
% 0.94/1.15 Here is a proof with depth 12, length 158 :
% 0.94/1.15 % SZS output start Refutation
% 0.94/1.15 4[0:Inp] || -> group_element(e_1)*.
% 0.94/1.15 5[0:Inp] || -> group_element(e_2)*.
% 0.94/1.15 6[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.94/1.15 7[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.94/1.15 8[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_2) product(v,u,e_1)*.
% 0.94/1.15 9[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.94/1.15 10[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.94/1.15 11[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.94/1.15 12[0:Inp] || product(u,v,w)*+ product(u,x,y)* product(v,w,z)* product(x,y,z)* -> equalish(x,v)*.
% 0.94/1.15 13[0:Inp] || product(u,v,w)*+ product(u,x,y)* product(v,w,z)* product(x,y,z)* -> equalish(y,w)*.
% 0.94/1.15 17[0:Res:12.4,6.0] || product(u,e_2,v)*+ product(u,e_1,w)* product(e_2,v,x)* product(e_1,w,x)* -> .
% 0.94/1.15 21[0:Res:8.3,9.0] group_element(u) group_element(v) || product(v,u,w)*+ -> product(v,u,e_2)* equalish(w,e_1).
% 0.94/1.15 22[0:Res:8.3,10.0] group_element(u) group_element(v) || product(v,w,e_1)*+ -> product(v,u,e_2)* equalish(w,u)*.
% 0.94/1.15 23[0:Res:8.3,11.0] group_element(u) group_element(v) || product(w,u,e_1)*+ -> product(v,u,e_2)* equalish(w,v)*.
% 0.94/1.15 25[0:Res:8.3,21.2] group_element(u) group_element(v) group_element(u) group_element(v) || -> product(v,u,e_2)* product(v,u,e_2)* equalish(e_1,e_1).
% 0.94/1.15 26[0:Obv:25.4] group_element(u) group_element(v) || -> product(v,u,e_2)* equalish(e_1,e_1).
% 0.94/1.15 27[1:Spt:26.0,26.1,26.2] group_element(u) group_element(v) || -> product(v,u,e_2)*.
% 0.94/1.15 30[1:Res:27.2,10.0] group_element(u) group_element(v) || product(v,w,e_2)*+ -> equalish(w,u)*.
% 0.94/1.15 41[1:Res:27.2,30.2] group_element(u) group_element(v) group_element(w) group_element(v) || -> equalish(u,w)*.
% 0.94/1.15 42[1:Obv:41.1] group_element(u) group_element(v) group_element(w) || -> equalish(u,v)*.
% 0.94/1.15 43[1:Con:42.2] group_element(u) group_element(v) || -> equalish(u,v)*.
% 0.94/1.15 45[1:Res:43.2,6.0] group_element(e_1) group_element(e_2) || -> .
% 0.94/1.15 47[1:SSi:45.1,45.0,5.0,4.0] || -> .
% 0.94/1.15 48[1:Spt:47.0,26.3] || -> equalish(e_1,e_1)*.
% 0.94/1.15 51[0:Res:8.3,13.0] group_element(u) group_element(v) || product(v,w,x)*+ product(u,e_1,y)* product(w,x,y)* -> product(v,u,e_2)* equalish(x,e_1).
% 0.94/1.15 57[0:Res:8.3,22.2] group_element(u) group_element(v) group_element(w) group_element(v) || -> product(v,u,e_2)* product(v,w,e_2)* equalish(u,w)*.
% 0.94/1.15 58[0:Obv:57.1] group_element(u) group_element(v) group_element(w) || -> product(w,u,e_2)* product(w,v,e_2)* equalish(u,v)*.
% 0.94/1.15 59[0:Res:8.3,23.2] group_element(u) group_element(v) group_element(u) group_element(w) || -> product(v,u,e_2)* product(w,u,e_2)* equalish(v,w)*.
% 0.94/1.15 60[0:Obv:59.0] group_element(u) group_element(v) group_element(w) || -> product(u,v,e_2)* product(w,v,e_2)* equalish(u,w)*.
% 0.94/1.15 61[0:Res:8.3,17.0] group_element(e_2) group_element(u) || product(u,e_1,v)* product(e_2,e_1,w) product(e_1,v,w)* -> product(u,e_2,e_2).
% 0.94/1.15 62[0:SSi:61.0,5.0] group_element(u) || product(u,e_1,v)*+ product(e_2,e_1,w) product(e_1,v,w)* -> product(u,e_2,e_2).
% 0.94/1.15 66[0:Fac:58.3,58.4] group_element(u) group_element(u) group_element(v) || -> product(v,u,e_2)* equalish(u,u)*.
% 0.94/1.15 87[0:Obv:66.0] group_element(u) group_element(v) || -> product(v,u,e_2)* equalish(u,u)*.
% 0.94/1.15 105[0:Res:87.2,17.0] group_element(e_2) group_element(u) || product(u,e_1,v)* product(e_2,e_2,w) product(e_1,v,w)* -> equalish(e_2,e_2).
% 0.94/1.15 109[0:SSi:105.0,5.0] group_element(u) || product(u,e_1,v)*+ product(e_2,e_2,w) product(e_1,v,w)* -> equalish(e_2,e_2).
% 0.94/1.15 169[0:Res:8.3,109.1] group_element(e_1) group_element(u) group_element(u) || product(e_2,e_2,v) product(e_1,e_1,v)* -> product(u,e_1,e_2)* equalish(e_2,e_2).
% 0.94/1.15 170[0:Obv:169.1] group_element(e_1) group_element(u) || product(e_2,e_2,v) product(e_1,e_1,v)* -> product(u,e_1,e_2)* equalish(e_2,e_2).
% 0.94/1.15 171[0:SSi:170.0,4.0] group_element(u) || product(e_2,e_2,v)+ product(e_1,e_1,v)* -> product(u,e_1,e_2)* equalish(e_2,e_2).
% 0.94/1.15 178[2:Spt:171.0,171.3] group_element(u) || -> product(u,e_1,e_2)*.
% 0.94/1.15 184[2:Res:178.1,11.0] group_element(u) || product(v,e_1,e_2)*+ -> equalish(v,u)*.
% 0.94/1.15 201[0:Res:8.3,62.1] group_element(e_1) group_element(u) group_element(u) || product(e_2,e_1,v) product(e_1,e_1,v)* -> product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.94/1.15 203[0:Obv:201.1] group_element(e_1) group_element(u) || product(e_2,e_1,v) product(e_1,e_1,v)* -> product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.94/1.15 247[2:Res:178.1,184.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 0.94/1.15 250[2:Res:247.2,6.0] group_element(e_1) group_element(e_2) || -> .
% 0.94/1.15 252[2:SSi:250.1,250.0,5.0,4.0] || -> .
% 0.94/1.15 253[2:Spt:252.0,171.1,171.2,171.4] || product(e_2,e_2,u)+ product(e_1,e_1,u)* -> equalish(e_2,e_2).
% 0.94/1.15 254[0:SSi:203.0,4.0] group_element(u) || product(e_2,e_1,v)+ product(e_1,e_1,v)* -> product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.94/1.15 342[0:Res:8.3,254.1] group_element(e_1) group_element(e_2) group_element(u) || product(e_1,e_1,e_1)* -> product(e_2,e_1,e_2) product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.94/1.15 343[0:SSi:342.1,342.0,5.0,4.0] group_element(u) || product(e_1,e_1,e_1)*+ -> product(e_2,e_1,e_2) product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.94/1.15 348[3:Spt:343.0,343.3,343.4] group_element(u) || -> product(u,e_1,e_2)* product(u,e_2,e_2).
% 0.94/1.15 352[3:Res:348.1,9.0] group_element(u) || product(u,e_1,v)*+ -> product(u,e_2,e_2) equalish(v,e_2).
% 0.94/1.15 356[3:Res:348.1,62.1] group_element(u) group_element(u) || product(e_2,e_1,v) product(e_1,e_2,v)* -> product(u,e_2,e_2)* product(u,e_2,e_2)*.
% 0.94/1.15 363[3:Obv:356.4] group_element(u) || product(e_2,e_1,v)+ product(e_1,e_2,v)* -> product(u,e_2,e_2)*.
% 0.94/1.15 373[3:Res:348.1,352.1] group_element(u) group_element(u) || -> product(u,e_2,e_2)* product(u,e_2,e_2)* equalish(e_2,e_2).
% 0.94/1.15 375[3:Obv:373.2] group_element(u) || -> product(u,e_2,e_2)* equalish(e_2,e_2).
% 0.94/1.15 381[4:Spt:375.0,375.1] group_element(u) || -> product(u,e_2,e_2)*.
% 0.94/1.15 386[4:Res:381.1,11.0] group_element(u) || product(v,e_2,e_2)*+ -> equalish(v,u)*.
% 0.94/1.15 428[4:Res:381.1,386.1] group_element(u) group_element(v) || -> equalish(u,v)*.
% 0.94/1.15 431[4:Res:428.2,6.0] group_element(e_1) group_element(e_2) || -> .
% 0.94/1.15 433[4:SSi:431.1,431.0,5.0,4.0] || -> .
% 0.94/1.15 434[4:Spt:433.0,375.2] || -> equalish(e_2,e_2)*.
% 0.94/1.15 501[3:Res:348.1,363.1] group_element(e_2) group_element(u) || product(e_1,e_2,e_2)* -> product(e_2,e_2,e_2) product(u,e_2,e_2)*.
% 0.94/1.15 502[3:Res:8.3,363.1] group_element(e_1) group_element(e_2) group_element(u) || product(e_1,e_2,e_1)* -> product(e_2,e_1,e_2) product(u,e_2,e_2)*.
% 0.94/1.15 503[3:Con:501.1] group_element(e_2) || product(e_1,e_2,e_2)* -> product(e_2,e_2,e_2).
% 0.94/1.15 504[3:SSi:503.0,5.0] || product(e_1,e_2,e_2)*+ -> product(e_2,e_2,e_2).
% 0.94/1.15 505[3:SSi:502.1,502.0,5.0,4.0] group_element(u) || product(e_1,e_2,e_1)*+ -> product(e_2,e_1,e_2) product(u,e_2,e_2)*.
% 0.94/1.15 554[3:Res:58.3,504.0] group_element(e_2) group_element(u) group_element(e_1) || -> product(e_1,u,e_2)* equalish(e_2,u) product(e_2,e_2,e_2).
% 0.94/1.15 556[3:Res:58.4,504.0] group_element(u) group_element(e_2) group_element(e_1) || -> product(e_1,u,e_2)* equalish(u,e_2) product(e_2,e_2,e_2).
% 0.94/1.15 559[3:SSi:556.2,556.1,4.0,5.0] group_element(u) || -> product(e_1,u,e_2)* equalish(u,e_2) product(e_2,e_2,e_2).
% 0.94/1.15 561[3:SSi:554.2,554.0,4.0,5.0] group_element(u) || -> product(e_1,u,e_2)* equalish(e_2,u) product(e_2,e_2,e_2).
% 0.94/1.15 580[5:Spt:559.0,559.1,559.2] group_element(u) || -> product(e_1,u,e_2)* equalish(u,e_2).
% 0.94/1.15 586[5:Res:580.1,11.0] group_element(u) || product(v,u,e_2)*+ -> equalish(u,e_2) equalish(v,e_1).
% 0.94/1.15 638[6:Spt:561.0,561.1,561.2] group_element(u) || -> product(e_1,u,e_2)* equalish(e_2,u).
% 0.94/1.15 643[6:Res:638.1,10.0] group_element(u) || product(e_1,v,e_2)*+ -> equalish(e_2,u)* equalish(v,u)*.
% 0.94/1.15 995[7:Spt:505.0,505.3] group_element(u) || -> product(u,e_2,e_2)*.
% 0.94/1.15 1018[7:Res:995.1,643.1] group_element(e_1) group_element(u) || -> equalish(e_2,u)* equalish(e_2,u)*.
% 0.94/1.15 1035[7:Obv:1018.2] group_element(e_1) group_element(u) || -> equalish(e_2,u)*.
% 0.94/1.15 1036[7:SSi:1035.0,4.0] group_element(u) || -> equalish(e_2,u)*.
% 1.13/1.30 1074[7:Res:1036.1,7.0] group_element(e_1) || -> .
% 1.13/1.30 1075[7:SSi:1074.0,4.0] || -> .
% 1.13/1.30 1076[7:Spt:1075.0,505.1,505.2] || product(e_1,e_2,e_1)*+ -> product(e_2,e_1,e_2).
% 1.13/1.30 1078[7:Res:8.3,1076.0] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_2)* product(e_2,e_1,e_2).
% 1.13/1.30 1079[7:SSi:1078.1,1078.0,4.0,5.0] || -> product(e_1,e_2,e_2)* product(e_2,e_1,e_2).
% 1.13/1.30 1080[8:Spt:1079.1] || -> product(e_2,e_1,e_2)*.
% 1.13/1.30 1088[8:Res:1080.0,586.1] group_element(e_1) || -> equalish(e_1,e_2)* equalish(e_2,e_1).
% 1.13/1.30 1099[8:SSi:1088.0,4.0] || -> equalish(e_1,e_2)* equalish(e_2,e_1).
% 1.13/1.30 1100[8:MRR:1099.0,1099.1,6.0,7.0] || -> .
% 1.13/1.30 1107[8:Spt:1100.0,1079.1,1080.0] || product(e_2,e_1,e_2)*+ -> .
% 1.13/1.30 1108[8:Spt:1100.0,1079.0] || -> product(e_1,e_2,e_2)*.
% 1.13/1.30 1118[8:Res:1108.0,10.0] || product(e_1,u,e_2)* -> equalish(u,e_2).
% 1.13/1.30 1133[8:MRR:580.1,1118.0] group_element(u) || -> equalish(u,e_2)*.
% 1.13/1.30 1169[8:Res:1133.1,6.0] group_element(e_1) || -> .
% 1.13/1.30 1170[8:SSi:1169.0,4.0] || -> .
% 1.13/1.30 1171[6:Spt:1170.0,561.3] || -> product(e_2,e_2,e_2)*.
% 1.13/1.30 1179[6:Res:1171.0,10.0] || product(e_2,u,e_2)*+ -> equalish(u,e_2).
% 1.13/1.30 1180[6:Res:1171.0,11.0] || product(u,e_2,e_2)*+ -> equalish(u,e_2).
% 1.13/1.30 1658[7:Spt:505.0,505.3] group_element(u) || -> product(u,e_2,e_2)*.
% 1.13/1.30 1686[7:Res:1658.1,1180.0] group_element(u) || -> equalish(u,e_2)*.
% 1.13/1.30 1710[7:Res:1686.1,6.0] group_element(e_1) || -> .
% 1.13/1.30 1711[7:SSi:1710.0,4.0] || -> .
% 1.13/1.30 1712[7:Spt:1711.0,505.1,505.2] || product(e_1,e_2,e_1)*+ -> product(e_2,e_1,e_2).
% 1.13/1.30 1713[7:Res:8.3,1712.0] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_2)* product(e_2,e_1,e_2).
% 1.13/1.30 1714[7:SSi:1713.1,1713.0,4.0,5.0] || -> product(e_1,e_2,e_2)* product(e_2,e_1,e_2).
% 1.13/1.30 1725[8:Spt:1714.1] || -> product(e_2,e_1,e_2)*.
% 1.13/1.30 1748[8:Res:1725.0,1179.0] || -> equalish(e_1,e_2)*.
% 1.13/1.30 1750[8:MRR:1748.0,6.0] || -> .
% 1.13/1.30 1764[8:Spt:1750.0,1714.1,1725.0] || product(e_2,e_1,e_2)* -> .
% 1.13/1.30 1765[8:Spt:1750.0,1714.0] || -> product(e_1,e_2,e_2)*.
% 1.13/1.30 1792[8:Res:1765.0,1180.0] || -> equalish(e_1,e_2)*.
% 1.13/1.30 1793[8:MRR:1792.0,6.0] || -> .
% 1.13/1.30 1804[5:Spt:1793.0,559.3] || -> product(e_2,e_2,e_2)*.
% 1.13/1.30 1808[5:Res:1804.0,10.0] || product(e_2,u,e_2)*+ -> equalish(u,e_2).
% 1.13/1.30 1809[5:Res:1804.0,11.0] || product(u,e_2,e_2)*+ -> equalish(u,e_2).
% 1.13/1.30 2065[6:Spt:505.0,505.3] group_element(u) || -> product(u,e_2,e_2)*.
% 1.13/1.30 2088[6:Res:2065.1,1809.0] group_element(u) || -> equalish(u,e_2)*.
% 1.13/1.30 2108[6:Res:2088.1,6.0] group_element(e_1) || -> .
% 1.13/1.30 2109[6:SSi:2108.0,4.0] || -> .
% 1.13/1.30 2110[6:Spt:2109.0,505.1,505.2] || product(e_1,e_2,e_1)*+ -> product(e_2,e_1,e_2).
% 1.13/1.30 2111[6:Res:8.3,2110.0] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_2)* product(e_2,e_1,e_2).
% 1.13/1.30 2112[6:SSi:2111.1,2111.0,4.0,5.0] || -> product(e_1,e_2,e_2)* product(e_2,e_1,e_2).
% 1.13/1.30 2191[7:Spt:2112.1] || -> product(e_2,e_1,e_2)*.
% 1.13/1.30 2212[7:Res:2191.0,1808.0] || -> equalish(e_1,e_2)*.
% 1.13/1.30 2213[7:MRR:2212.0,6.0] || -> .
% 1.13/1.30 2226[7:Spt:2213.0,2112.1,2191.0] || product(e_2,e_1,e_2)* -> .
% 1.13/1.30 2227[7:Spt:2213.0,2112.0] || -> product(e_1,e_2,e_2)*.
% 1.13/1.30 2252[7:Res:2227.0,1809.0] || -> equalish(e_1,e_2)*.
% 1.13/1.30 2253[7:MRR:2252.0,6.0] || -> .
% 1.13/1.30 2264[3:Spt:2253.0,343.1,343.2] || product(e_1,e_1,e_1)*+ -> product(e_2,e_1,e_2).
% 1.13/1.30 2269[3:Res:8.3,2264.0] group_element(e_1) group_element(e_1) || -> product(e_1,e_1,e_2)* product(e_2,e_1,e_2).
% 1.13/1.30 2270[3:Obv:2269.0] group_element(e_1) || -> product(e_1,e_1,e_2)* product(e_2,e_1,e_2).
% 1.13/1.30 2271[3:SSi:2270.0,4.0] || -> product(e_1,e_1,e_2)* product(e_2,e_1,e_2).
% 1.13/1.30 2272[4:Spt:2271.1] || -> product(e_2,e_1,e_2)*.
% 1.13/1.30 2277[4:Res:2272.0,10.0] || product(e_2,u,e_2)*+ -> equalish(u,e_1).
% 1.13/1.30 2283[4:Res:2272.0,51.2] group_element(u) group_element(e_2) || product(u,e_1,v)* product(e_1,e_2,v)* -> product(e_2,u,e_2)* equalish(e_2,e_1).
% 1.13/1.30 2300[4:SSi:2283.1,5.0] group_element(u) || product(u,e_1,v)* product(e_1,e_2,v)* -> product(e_2,u,e_2)* equalish(e_2,e_1).
% 1.13/1.30 2301[4:MRR:2300.4,7.0] group_element(u) || product(u,e_1,v)*+ product(e_1,e_2,v)* -> product(e_2,u,e_2)*.
% 1.13/1.30 2322[4:Res:60.4,2277.0] group_element(u) group_element(v) group_element(e_2) || -> product(u,v,e_2)* equalish(u,e_2) equalish(v,e_1).
% 1.13/1.30 2327[4:SSi:2322.2,5.0] group_element(u) group_element(v) || -> product(u,v,e_2)* equalish(u,e_2) equalish(v,e_1).
% 1.13/1.30 3102[4:Res:2272.0,2301.1] group_element(e_2) || product(e_1,e_2,e_2)* -> product(e_2,e_2,e_2).
% 1.13/1.30 3107[4:SSi:3102.0,5.0] || product(e_1,e_2,e_2)*+ -> product(e_2,e_2,e_2).
% 1.13/1.30 3131[4:Res:2327.2,3107.0] group_element(e_1) group_element(e_2) || -> equalish(e_1,e_2) equalish(e_2,e_1) product(e_2,e_2,e_2)*.
% 1.13/1.30 3136[4:SSi:3131.1,3131.0,5.0,4.0] || -> equalish(e_1,e_2) equalish(e_2,e_1) product(e_2,e_2,e_2)*.
% 1.13/1.30 3137[4:MRR:3136.0,3136.1,6.0,7.0] || -> product(e_2,e_2,e_2)*.
% 1.13/1.30 3162[4:Res:3137.0,2277.0] || -> equalish(e_2,e_1)*.
% 1.13/1.30 3163[4:MRR:3162.0,7.0] || -> .
% 1.13/1.30 3178[4:Spt:3163.0,2271.1,2272.0] || product(e_2,e_1,e_2)*+ -> .
% 1.13/1.30 3179[4:Spt:3163.0,2271.0] || -> product(e_1,e_1,e_2)*.
% 1.13/1.30 3201[4:Res:3179.0,10.0] || product(e_1,u,e_2)*+ -> equalish(u,e_1).
% 1.13/1.30 3205[4:Res:3179.0,62.1] group_element(e_1) || product(e_2,e_1,u) product(e_1,e_2,u)* -> product(e_1,e_2,e_2)*.
% 1.13/1.30 3222[4:SSi:3205.0,4.0] || product(e_2,e_1,u)+ product(e_1,e_2,u)* -> product(e_1,e_2,e_2)*.
% 1.13/1.30 3473[4:Res:8.3,3222.0] group_element(e_1) group_element(e_2) || product(e_1,e_2,e_1)* -> product(e_2,e_1,e_2) product(e_1,e_2,e_2).
% 1.13/1.30 3476[4:SSi:3473.1,3473.0,5.0,4.0] || product(e_1,e_2,e_1)* -> product(e_2,e_1,e_2) product(e_1,e_2,e_2).
% 1.13/1.30 3477[4:MRR:3476.1,3178.0] || product(e_1,e_2,e_1)*+ -> product(e_1,e_2,e_2).
% 1.13/1.30 3478[4:Res:8.3,3477.0] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_2)* product(e_1,e_2,e_2)*.
% 1.13/1.30 3479[4:Obv:3478.2] group_element(e_2) group_element(e_1) || -> product(e_1,e_2,e_2)*.
% 1.13/1.30 3480[4:SSi:3479.1,3479.0,4.0,5.0] || -> product(e_1,e_2,e_2)*.
% 1.13/1.30 3514[4:Res:3480.0,3201.0] || -> equalish(e_2,e_1)*.
% 1.13/1.30 3515[4:MRR:3514.0,7.0] || -> .
% 1.13/1.30 % SZS output end Refutation
% 1.13/1.30 Formulae used in the proof : element_1 element_2 e_1_is_not_e_2 e_2_is_not_e_1 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation qg2_1 qg2_2
% 1.13/1.30
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