TSTP Solution File: GRP126-1.004 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP126-1.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:45:36 EDT 2022
% Result : Unsatisfiable 0.14s 0.41s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP126-1.004 : TPTP v8.1.0. Released v1.2.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 07:47:55 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.41
% 0.14/0.41 SPASS V 3.9
% 0.14/0.41 SPASS beiseite: Proof found.
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41 SPASS derived 238 clauses, backtracked 39 clauses, performed 6 splits and kept 170 clauses.
% 0.14/0.41 SPASS allocated 75832 KBytes.
% 0.14/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.14/0.41 0:00:00.02 for the input.
% 0.14/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.41 0:00:00.00 for inferences.
% 0.14/0.41 0:00:00.00 for the backtracking.
% 0.14/0.41 0:00:00.01 for the reduction.
% 0.14/0.41
% 0.14/0.41
% 0.14/0.41 Here is a proof with depth 12, length 81 :
% 0.14/0.41 % SZS output start Refutation
% 0.14/0.41 1[0:Inp] || -> group_element(e_1)*.
% 0.14/0.41 2[0:Inp] || -> group_element(e_2)*.
% 0.14/0.41 3[0:Inp] || -> group_element(e_3)*.
% 0.14/0.41 4[0:Inp] || -> group_element(e_4)*.
% 0.14/0.41 5[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.14/0.41 6[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.14/0.41 7[0:Inp] || equalish(e_1,e_4)*+ -> .
% 0.14/0.41 8[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.14/0.41 9[0:Inp] || equalish(e_2,e_3)*+ -> .
% 0.14/0.41 10[0:Inp] || equalish(e_2,e_4)*+ -> .
% 0.14/0.41 12[0:Inp] || equalish(e_3,e_2)*+ -> .
% 0.14/0.41 14[0:Inp] || equalish(e_4,e_1)*+ -> .
% 0.14/0.41 15[0:Inp] || equalish(e_4,e_2)*+ -> .
% 0.14/0.41 16[0:Inp] || equalish(e_4,e_3)*+ -> .
% 0.14/0.41 17[0:Inp] group_element(u) group_element(v) || -> product(v,u,e_4) product(v,u,e_3) product(v,u,e_2) product(v,u,e_1)*.
% 0.14/0.41 18[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.14/0.41 19[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.14/0.41 20[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.14/0.41 21[0:Inp] || -> product(u,u,u)*.
% 0.14/0.41 22[0:Inp] || product(u,v,w)*+ product(v,u,x)* -> product(x,w,u)*.
% 0.14/0.41 31[0:Res:21.0,20.0] || product(u,v,v)*+ -> equalish(u,v).
% 0.14/0.41 33[0:Res:21.0,19.0] || product(u,v,u)*+ -> equalish(v,u).
% 0.14/0.41 35[0:Res:21.0,18.0] || product(u,u,v)*+ -> equalish(v,u).
% 0.14/0.41 41[0:Res:17.5,33.0] group_element(u) group_element(e_1) || -> product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 0.14/0.41 45[0:Res:17.5,20.0] group_element(u) group_element(v) || product(w,u,e_1)*+ -> product(v,u,e_4) product(v,u,e_3) product(v,u,e_2)* equalish(w,v)*.
% 0.14/0.41 46[0:Res:17.5,31.0] group_element(e_1) group_element(u) || -> product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(u,e_1).
% 0.14/0.41 47[0:SSi:46.0,1.0] group_element(u) || -> product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(u,e_1).
% 0.14/0.41 48[0:SSi:41.1,1.0] group_element(u) || -> product(e_1,u,e_4) product(e_1,u,e_3) product(e_1,u,e_2)* equalish(u,e_1).
% 0.14/0.41 55[0:Res:47.3,33.0] group_element(e_2) || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.14/0.41 60[0:SSi:55.0,2.0] || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.14/0.41 61[0:MRR:60.2,60.3,8.0,5.0] || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)*.
% 0.14/0.41 62[0:Res:21.0,45.2] group_element(e_1) group_element(u) || -> product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_1,u).
% 0.14/0.41 64[0:SSi:62.0,1.0] group_element(u) || -> product(u,e_1,e_4) product(u,e_1,e_3) product(u,e_1,e_2)* equalish(e_1,u).
% 0.14/0.41 66[0:Res:61.1,22.0] || product(e_1,e_2,u)*+ -> product(e_2,e_1,e_4) product(u,e_3,e_2)*.
% 0.14/0.41 67[0:Res:61.1,18.0] || product(e_2,e_1,u)*+ -> product(e_2,e_1,e_4)* equalish(u,e_3).
% 0.14/0.41 69[0:Res:61.1,20.0] || product(u,e_1,e_3)*+ -> product(e_2,e_1,e_4)* equalish(u,e_2).
% 0.14/0.41 70[1:Spt:67.0,67.2] || product(e_2,e_1,u)*+ -> equalish(u,e_3).
% 0.14/0.41 76[2:Spt:69.0,69.2] || product(u,e_1,e_3)*+ -> equalish(u,e_2).
% 0.14/0.41 91[0:Res:48.3,31.0] group_element(e_2) || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.14/0.41 93[0:SSi:91.0,2.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.14/0.41 94[0:MRR:93.2,93.3,8.0,5.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)*.
% 0.14/0.41 99[0:Res:94.1,66.0] || -> product(e_1,e_2,e_4)* product(e_2,e_1,e_4) product(e_3,e_3,e_2).
% 0.14/0.41 100[3:Spt:99.1] || -> product(e_2,e_1,e_4)*.
% 0.14/0.41 105[3:Res:100.0,70.0] || -> equalish(e_4,e_3)*.
% 0.14/0.41 106[3:MRR:105.0,16.0] || -> .
% 0.14/0.41 107[3:Spt:106.0,99.1,100.0] || product(e_2,e_1,e_4)*+ -> .
% 0.14/0.41 108[3:Spt:106.0,99.0,99.2] || -> product(e_1,e_2,e_4)* product(e_3,e_3,e_2).
% 0.14/0.41 110[3:MRR:66.1,107.0] || product(e_1,e_2,u)*+ -> product(u,e_3,e_2)*.
% 0.14/0.41 111[4:Spt:108.0] || -> product(e_1,e_2,e_4)*.
% 0.14/0.41 140[4:Res:111.0,110.0] || -> product(e_4,e_3,e_2)*.
% 0.14/0.41 144[4:Res:140.0,19.0] || product(e_4,u,e_2)*+ -> equalish(u,e_3).
% 0.14/0.41 148[4:Res:47.3,144.0] group_element(e_4) || -> product(e_4,e_1,e_4) product(e_4,e_1,e_3)* equalish(e_4,e_1) equalish(e_1,e_3).
% 0.14/0.41 150[4:SSi:148.0,4.0] || -> product(e_4,e_1,e_4) product(e_4,e_1,e_3)* equalish(e_4,e_1) equalish(e_1,e_3).
% 0.14/0.41 151[4:MRR:150.2,150.3,14.0,6.0] || -> product(e_4,e_1,e_4) product(e_4,e_1,e_3)*.
% 0.14/0.41 169[4:Res:151.1,76.0] || -> product(e_4,e_1,e_4)* equalish(e_4,e_2).
% 0.14/0.41 170[4:MRR:169.1,15.0] || -> product(e_4,e_1,e_4)*.
% 0.14/0.41 173[4:Res:170.0,33.0] || -> equalish(e_1,e_4)*.
% 0.14/0.41 179[4:MRR:173.0,7.0] || -> .
% 0.14/0.41 181[4:Spt:179.0,108.0,111.0] || product(e_1,e_2,e_4)* -> .
% 0.14/0.41 182[4:Spt:179.0,108.1] || -> product(e_3,e_3,e_2)*.
% 0.14/0.41 188[4:Res:182.0,35.0] || -> equalish(e_2,e_3)*.
% 0.14/0.41 197[4:MRR:188.0,9.0] || -> .
% 0.14/0.41 200[2:Spt:197.0,69.1] || -> product(e_2,e_1,e_4)*.
% 0.14/0.41 207[2:Res:200.0,70.0] || -> equalish(e_4,e_3)*.
% 0.14/0.41 208[2:MRR:207.0,16.0] || -> .
% 0.14/0.41 209[1:Spt:208.0,67.1] || -> product(e_2,e_1,e_4)*.
% 0.14/0.41 212[1:Res:209.0,22.0] || product(e_1,e_2,u)*+ -> product(u,e_4,e_2)*.
% 0.14/0.41 215[1:Res:209.0,20.0] || product(u,e_1,e_4)*+ -> equalish(u,e_2).
% 0.14/0.41 216[2:Spt:94.0] || -> product(e_1,e_2,e_4)*.
% 0.14/0.41 264[2:Res:216.0,212.0] || -> product(e_4,e_4,e_2)*.
% 0.14/0.41 265[2:Res:264.0,35.0] || -> equalish(e_2,e_4)*.
% 0.14/0.41 274[2:MRR:265.0,10.0] || -> .
% 0.14/0.41 277[2:Spt:274.0,94.0,216.0] || product(e_1,e_2,e_4)*+ -> .
% 0.14/0.41 278[2:Spt:274.0,94.1] || -> product(e_1,e_2,e_3)*.
% 0.14/0.41 289[2:Res:278.0,212.0] || -> product(e_3,e_4,e_2)*.
% 0.14/0.41 294[2:Res:289.0,19.0] || product(e_3,u,e_2)*+ -> equalish(u,e_4).
% 0.14/0.41 317[2:Res:64.3,294.0] group_element(e_3) || -> product(e_3,e_1,e_4) product(e_3,e_1,e_3)* equalish(e_1,e_3) equalish(e_1,e_4).
% 0.14/0.41 321[2:SSi:317.0,3.0] || -> product(e_3,e_1,e_4) product(e_3,e_1,e_3)* equalish(e_1,e_3) equalish(e_1,e_4).
% 0.14/0.41 322[2:MRR:321.1,321.2,321.3,33.0,6.0,7.0] || -> product(e_3,e_1,e_4)*.
% 0.14/0.41 329[2:Res:322.0,215.0] || -> equalish(e_3,e_2)*.
% 0.14/0.41 330[2:MRR:329.0,12.0] || -> .
% 0.14/0.41 % SZS output end Refutation
% 0.14/0.41 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_2 e_4_is_not_e_1 e_4_is_not_e_2 e_4_is_not_e_3 product_total_function1 product_total_function2 product_right_cancellation product_left_cancellation product_idempotence qg4
% 0.14/0.41
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