TSTP Solution File: GRP124-3.004 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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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