TSTP Solution File: GRP124-3.004 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP124-3.004 : 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 11:45:31 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP124-3.004 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.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 09:53:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 494 clauses, backtracked 87 clauses, performed 9 splits and kept 381 clauses.
% 0.19/0.52 SPASS allocated 76076 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.52 0:00:00.04 for the input.
% 0.19/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.01 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.08 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 10, length 97 :
% 0.19/0.52 % SZS output start Refutation
% 0.19/0.52 22[0:Inp] || -> group_element(e_1)*.
% 0.19/0.52 23[0:Inp] || -> group_element(e_2)*.
% 0.19/0.52 24[0:Inp] || -> group_element(e_3)*.
% 0.19/0.52 25[0:Inp] || -> group_element(e_4)*.
% 0.19/0.52 26[0:Inp] || equalish(e_1,e_2)*+ -> .
% 0.19/0.52 27[0:Inp] || equalish(e_1,e_3)*+ -> .
% 0.19/0.52 29[0:Inp] || equalish(e_2,e_1)*+ -> .
% 0.19/0.52 30[0:Inp] || equalish(e_2,e_3)*+ -> .
% 0.19/0.52 32[0:Inp] || equalish(e_3,e_1)*+ -> .
% 0.19/0.52 33[0:Inp] || equalish(e_3,e_2)*+ -> .
% 0.19/0.52 35[0:Inp] || equalish(e_4,e_1)*+ -> .
% 0.19/0.52 36[0:Inp] || equalish(e_4,e_2)*+ -> .
% 0.19/0.52 37[0:Inp] || equalish(e_4,e_3)*+ -> .
% 0.19/0.52 38[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)*.
% 0.19/0.52 39[0:Inp] || product(u,v,w)*+ product(u,v,x)* -> equalish(x,w)*.
% 0.19/0.52 40[0:Inp] || product(u,v,w)*+ product(u,x,w)* -> equalish(x,v)*.
% 0.19/0.52 41[0:Inp] || product(u,v,w)*+ product(x,v,w)* -> equalish(x,u)*.
% 0.19/0.52 42[0:Inp] || -> product(u,u,u)*.
% 0.19/0.52 44[0:Inp] || product(u,v,w)*+ product(u,x,y)* product(v,w,z)* product(x,y,z)* -> equalish(y,w)*.
% 0.19/0.52 46[0:Res:42.0,44.1] || product(u,v,v)*+ product(u,w,x)* product(w,x,v)* -> equalish(x,v).
% 0.19/0.52 84[0:Res:42.0,41.0] || product(u,v,v)*+ -> equalish(u,v).
% 0.19/0.52 86[0:Res:42.0,40.0] || product(u,v,u)*+ -> equalish(v,u).
% 0.19/0.52 94[0:Res:42.0,46.0] || product(u,v,w)*+ product(v,w,u)* -> equalish(w,u).
% 0.19/0.52 112[0:Res:38.5,84.0] 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).
% 0.19/0.52 113[0:Res:38.5,86.0] 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).
% 0.19/0.52 117[0:SSi:113.1,22.0] 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).
% 0.19/0.52 118[0:SSi:112.0,22.0] 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).
% 0.19/0.52 132[0:Res:117.3,84.0] 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).
% 0.19/0.52 135[0:SSi:132.0,23.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.19/0.52 136[0:MRR:135.2,135.3,29.0,26.0] || -> product(e_1,e_2,e_4) product(e_1,e_2,e_3)*.
% 0.19/0.52 140[0:Res:136.1,94.0] || product(e_2,e_3,e_1) -> product(e_1,e_2,e_4)* equalish(e_3,e_1).
% 0.19/0.52 142[0:Res:136.1,39.0] || product(e_1,e_2,u)*+ -> product(e_1,e_2,e_4)* equalish(u,e_3).
% 0.19/0.52 145[0:MRR:140.2,32.0] || product(e_2,e_3,e_1)+ -> product(e_1,e_2,e_4)*.
% 0.19/0.52 147[0:Res:38.5,145.0] group_element(e_3) group_element(e_2) || -> product(e_2,e_3,e_4) product(e_2,e_3,e_3) product(e_2,e_3,e_2) product(e_1,e_2,e_4)*.
% 0.19/0.52 148[0:SSi:147.1,147.0,23.0,24.0] || -> product(e_2,e_3,e_4) product(e_2,e_3,e_3) product(e_2,e_3,e_2) product(e_1,e_2,e_4)*.
% 0.19/0.52 149[1:Spt:142.0,142.2] || product(e_1,e_2,u)*+ -> equalish(u,e_3).
% 0.19/0.52 171[1:Res:148.3,149.0] || -> product(e_2,e_3,e_4) product(e_2,e_3,e_3) product(e_2,e_3,e_2)* equalish(e_4,e_3).
% 0.19/0.52 172[1:MRR:171.3,37.0] || -> product(e_2,e_3,e_4) product(e_2,e_3,e_3) product(e_2,e_3,e_2)*.
% 0.19/0.52 184[1:Res:172.2,86.0] || -> product(e_2,e_3,e_4) product(e_2,e_3,e_3)* equalish(e_3,e_2).
% 0.19/0.52 185[1:MRR:184.2,33.0] || -> product(e_2,e_3,e_4) product(e_2,e_3,e_3)*.
% 0.19/0.52 195[1:Res:185.1,84.0] || -> product(e_2,e_3,e_4)* equalish(e_2,e_3).
% 0.19/0.52 196[1:MRR:195.1,30.0] || -> product(e_2,e_3,e_4)*.
% 0.19/0.52 202[1:Res:196.0,40.0] || product(e_2,u,e_4)*+ -> equalish(u,e_3).
% 0.19/0.52 203[1:Res:196.0,41.0] || product(u,e_3,e_4)*+ -> equalish(u,e_2).
% 0.19/0.52 237[0:Res:118.3,86.0] 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).
% 0.19/0.52 241[0:SSi:237.0,23.0] || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)* equalish(e_2,e_1) equalish(e_1,e_2).
% 0.19/0.52 242[0:MRR:241.2,241.3,29.0,26.0] || -> product(e_2,e_1,e_4) product(e_2,e_1,e_3)*.
% 0.19/0.52 247[0:Res:242.1,94.0] || product(e_1,e_3,e_2)* -> product(e_2,e_1,e_4) equalish(e_3,e_2).
% 0.19/0.52 254[0:MRR:247.2,33.0] || product(e_1,e_3,e_2)*+ -> product(e_2,e_1,e_4).
% 0.19/0.52 258[0:Res:117.3,254.0] group_element(e_3) || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3)* equalish(e_3,e_1) product(e_2,e_1,e_4).
% 0.19/0.52 259[0:SSi:258.0,24.0] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3)* equalish(e_3,e_1) product(e_2,e_1,e_4).
% 0.19/0.52 260[0:MRR:259.2,32.0] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3)* product(e_2,e_1,e_4).
% 0.19/0.52 268[2:Spt:260.2] || -> product(e_2,e_1,e_4)*.
% 0.19/0.52 280[2:Res:268.0,202.0] || -> equalish(e_1,e_3)*.
% 0.19/0.52 281[2:MRR:280.0,27.0] || -> .
% 0.19/0.52 285[2:Spt:281.0,260.2,268.0] || product(e_2,e_1,e_4)* -> .
% 0.19/0.52 286[2:Spt:281.0,260.0,260.1] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3)*.
% 0.19/0.52 310[2:Res:286.1,84.0] || -> product(e_1,e_3,e_4)* equalish(e_1,e_3).
% 0.19/0.52 312[2:MRR:310.1,27.0] || -> product(e_1,e_3,e_4)*.
% 0.19/0.52 334[2:Res:312.0,203.0] || -> equalish(e_1,e_2)*.
% 0.19/0.52 335[2:MRR:334.0,26.0] || -> .
% 0.19/0.52 338[1:Spt:335.0,142.1] || -> product(e_1,e_2,e_4)*.
% 0.19/0.52 345[1:Res:338.0,94.0] || product(e_2,e_4,e_1)* -> equalish(e_4,e_1).
% 0.19/0.52 348[1:Res:338.0,40.0] || product(e_1,u,e_4)*+ -> equalish(u,e_2).
% 0.19/0.52 350[1:MRR:345.1,35.0] || product(e_2,e_4,e_1)*+ -> .
% 0.19/0.52 358[1:Res:38.5,350.0] group_element(e_4) group_element(e_2) || -> product(e_2,e_4,e_4) product(e_2,e_4,e_3) product(e_2,e_4,e_2)*.
% 0.19/0.52 359[1:SSi:358.1,358.0,23.0,25.0] || -> product(e_2,e_4,e_4) product(e_2,e_4,e_3) product(e_2,e_4,e_2)*.
% 0.19/0.52 360[2:Spt:242.0] || -> product(e_2,e_1,e_4)*.
% 0.19/0.52 367[2:Res:360.0,94.0] || product(e_1,e_4,e_2)* -> equalish(e_4,e_2).
% 0.19/0.52 370[2:Res:360.0,40.0] || product(e_2,u,e_4)*+ -> equalish(u,e_1).
% 0.19/0.52 374[2:MRR:367.1,36.0] || product(e_1,e_4,e_2)*+ -> .
% 0.19/0.52 378[2:Res:117.3,374.0] group_element(e_4) || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3)* equalish(e_4,e_1).
% 0.19/0.52 379[2:SSi:378.0,25.0] || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3)* equalish(e_4,e_1).
% 0.19/0.52 380[2:MRR:379.2,35.0] || -> product(e_1,e_4,e_4) product(e_1,e_4,e_3)*.
% 0.19/0.52 395[2:Res:380.1,39.0] || product(e_1,e_4,u)*+ -> product(e_1,e_4,e_4)* equalish(u,e_3).
% 0.19/0.52 397[2:Res:380.1,41.0] || product(u,e_4,e_3)*+ -> product(e_1,e_4,e_4)* equalish(u,e_1).
% 0.19/0.52 451[1:Res:359.2,86.0] || -> product(e_2,e_4,e_4) product(e_2,e_4,e_3)* equalish(e_4,e_2).
% 0.19/0.52 452[1:MRR:451.2,36.0] || -> product(e_2,e_4,e_4) product(e_2,e_4,e_3)*.
% 0.19/0.52 473[3:Spt:395.0,395.2] || product(e_1,e_4,u)*+ -> equalish(u,e_3).
% 0.19/0.52 483[4:Spt:397.0,397.2] || product(u,e_4,e_3)*+ -> equalish(u,e_1).
% 0.19/0.52 485[4:Res:452.1,483.0] || -> product(e_2,e_4,e_4)* equalish(e_2,e_1).
% 0.19/0.52 486[4:MRR:485.1,29.0] || -> product(e_2,e_4,e_4)*.
% 0.19/0.52 503[4:Res:486.0,370.0] || -> equalish(e_4,e_1)*.
% 0.19/0.52 505[4:MRR:503.0,35.0] || -> .
% 0.19/0.52 508[4:Spt:505.0,397.1] || -> product(e_1,e_4,e_4)*.
% 0.19/0.52 526[4:Res:508.0,473.0] || -> equalish(e_4,e_3)*.
% 0.19/0.52 529[4:MRR:526.0,37.0] || -> .
% 0.19/0.52 532[3:Spt:529.0,395.1] || -> product(e_1,e_4,e_4)*.
% 0.19/0.52 549[3:Res:532.0,348.0] || -> equalish(e_4,e_2)*.
% 0.19/0.52 551[3:MRR:549.0,36.0] || -> .
% 0.19/0.52 554[2:Spt:551.0,242.0,360.0] || product(e_2,e_1,e_4)*+ -> .
% 0.19/0.52 555[2:Spt:551.0,242.1] || -> product(e_2,e_1,e_3)*.
% 0.19/0.52 561[2:MRR:260.2,554.0] || -> product(e_1,e_3,e_4) product(e_1,e_3,e_3)*.
% 0.19/0.52 652[2:Res:561.1,84.0] || -> product(e_1,e_3,e_4)* equalish(e_1,e_3).
% 0.19/0.52 653[2:MRR:652.1,27.0] || -> product(e_1,e_3,e_4)*.
% 0.19/0.52 667[2:Res:653.0,348.0] || -> equalish(e_3,e_2)*.
% 0.19/0.52 668[2:MRR:667.0,33.0] || -> .
% 0.19/0.52 % SZS output end Refutation
% 0.19/0.52 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_2_is_not_e_1 e_2_is_not_e_3 e_3_is_not_e_1 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 qg2_2
% 0.19/0.52
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