TSTP Solution File: ANA003-4 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ANA003-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 : Thu Jul 14 19:28:33 EDT 2022

% Result   : Unsatisfiable 0.36s 0.54s
% Output   : Refutation 0.36s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA003-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n011.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 : Fri Jul  8 03:22:09 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.36/0.54  
% 0.36/0.54  SPASS V 3.9 
% 0.36/0.54  SPASS beiseite: Proof found.
% 0.36/0.54  % SZS status Theorem
% 0.36/0.54  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.36/0.54  SPASS derived 524 clauses, backtracked 14 clauses, performed 4 splits and kept 538 clauses.
% 0.36/0.54  SPASS allocated 64865 KBytes.
% 0.36/0.54  SPASS spent	0:00:00.18 on the problem.
% 0.36/0.54  		0:00:00.04 for the input.
% 0.36/0.54  		0:00:00.00 for the FLOTTER CNF translation.
% 0.36/0.54  		0:00:00.02 for inferences.
% 0.36/0.54  		0:00:00.00 for the backtracking.
% 0.36/0.54  		0:00:00.09 for the reduction.
% 0.36/0.54  
% 0.36/0.54  
% 0.36/0.54  Here is a proof with depth 10, length 34 :
% 0.36/0.54  % SZS output start Refutation
% 0.36/0.54  1[0:Inp] || less_or_equal(u,minimum(v,w))* -> less_or_equal(u,v).
% 0.36/0.54  2[0:Inp] || less_or_equal(u,minimum(v,w))* -> less_or_equal(u,w).
% 0.36/0.54  3[0:Inp] || less_or_equal(minimum(u,v),n0)* -> less_or_equal(v,n0) less_or_equal(u,n0).
% 0.36/0.54  4[0:Inp] || less_or_equal(u,half(v)) less_or_equal(w,half(v)) -> less_or_equal(add(w,u),v)*.
% 0.36/0.54  5[0:Inp] || less_or_equal(half(u),n0)* -> less_or_equal(u,n0).
% 0.36/0.54  6[0:Inp] || less_or_equal(delta_1(u),n0)* -> less_or_equal(u,n0).
% 0.36/0.54  7[0:Inp] || less_or_equal(delta_2(u),n0)* -> less_or_equal(u,n0).
% 0.36/0.54  8[0:Inp] || less_or_equal(absolute(add(u,negate(a_real_number))),delta_1(v)) -> less_or_equal(v,n0) less_or_equal(absolute(add(f(u),negate(f(a_real_number)))),v)*.
% 0.36/0.54  9[0:Inp] || less_or_equal(absolute(add(u,negate(a_real_number))),delta_2(v)) -> less_or_equal(v,n0) less_or_equal(absolute(add(g(u),negate(g(a_real_number)))),v)*.
% 0.36/0.54  10[0:Inp] || less_or_equal(epsilon_0,n0)* -> .
% 0.36/0.54  11[0:Inp] ||  -> less_or_equal(u,n0) less_or_equal(absolute(add(xs(u),negate(a_real_number))),u)*.
% 0.36/0.54  12[0:Inp] || less_or_equal(add(absolute(add(f(xs(u)),negate(f(a_real_number)))),absolute(add(g(xs(u)),negate(g(a_real_number))))),epsilon_0)* -> less_or_equal(u,n0).
% 0.36/0.54  14[0:Res:11.1,1.0] ||  -> less_or_equal(minimum(u,v),n0) less_or_equal(absolute(add(xs(minimum(u,v)),negate(a_real_number))),u)*.
% 0.36/0.54  15[0:Res:11.1,2.0] ||  -> less_or_equal(minimum(u,v),n0) less_or_equal(absolute(add(xs(minimum(u,v)),negate(a_real_number))),v)*.
% 0.36/0.54  55[0:Res:4.2,12.0] || less_or_equal(absolute(add(g(xs(u)),negate(g(a_real_number)))),half(epsilon_0)) less_or_equal(absolute(add(f(xs(u)),negate(f(a_real_number)))),half(epsilon_0))* -> less_or_equal(u,n0).
% 0.36/0.54  195[0:Res:8.2,55.1] || less_or_equal(absolute(add(xs(u),negate(a_real_number))),delta_1(half(epsilon_0))) less_or_equal(absolute(add(g(xs(u)),negate(g(a_real_number)))),half(epsilon_0))* -> less_or_equal(half(epsilon_0),n0) less_or_equal(u,n0).
% 0.36/0.54  480[1:Spt:195.0,195.1,195.3] || less_or_equal(absolute(add(xs(u),negate(a_real_number))),delta_1(half(epsilon_0))) less_or_equal(absolute(add(g(xs(u)),negate(g(a_real_number)))),half(epsilon_0))* -> less_or_equal(u,n0).
% 0.36/0.54  491[1:Res:9.2,480.1] || less_or_equal(absolute(add(xs(u),negate(a_real_number))),delta_2(half(epsilon_0))) less_or_equal(absolute(add(xs(u),negate(a_real_number))),delta_1(half(epsilon_0)))* -> less_or_equal(half(epsilon_0),n0) less_or_equal(u,n0).
% 0.36/0.54  522[2:Spt:491.0,491.1,491.3] || less_or_equal(absolute(add(xs(u),negate(a_real_number))),delta_2(half(epsilon_0))) less_or_equal(absolute(add(xs(u),negate(a_real_number))),delta_1(half(epsilon_0)))* -> less_or_equal(u,n0).
% 0.36/0.54  544[2:Res:15.1,522.1] || less_or_equal(absolute(add(xs(minimum(u,delta_1(half(epsilon_0)))),negate(a_real_number))),delta_2(half(epsilon_0)))* -> less_or_equal(minimum(u,delta_1(half(epsilon_0))),n0) less_or_equal(minimum(u,delta_1(half(epsilon_0))),n0).
% 0.36/0.54  555[2:Obv:544.1] || less_or_equal(absolute(add(xs(minimum(u,delta_1(half(epsilon_0)))),negate(a_real_number))),delta_2(half(epsilon_0)))* -> less_or_equal(minimum(u,delta_1(half(epsilon_0))),n0).
% 0.36/0.54  589[2:Res:14.1,555.0] ||  -> less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)* less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)*.
% 0.36/0.54  604[2:Obv:589.0] ||  -> less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)*.
% 0.36/0.54  619[2:Res:604.0,3.0] ||  -> less_or_equal(delta_1(half(epsilon_0)),n0)* less_or_equal(delta_2(half(epsilon_0)),n0).
% 0.36/0.54  620[2:Res:619.0,6.0] ||  -> less_or_equal(delta_2(half(epsilon_0)),n0)* less_or_equal(half(epsilon_0),n0).
% 0.36/0.54  621[2:MRR:620.0,7.0] ||  -> less_or_equal(half(epsilon_0),n0)*.
% 0.36/0.54  622[2:Res:621.0,5.0] ||  -> less_or_equal(epsilon_0,n0)*.
% 0.36/0.54  623[2:MRR:622.0,10.0] ||  -> .
% 0.36/0.54  624[2:Spt:623.0,491.2] ||  -> less_or_equal(half(epsilon_0),n0)*.
% 0.36/0.54  625[2:Res:624.0,5.0] ||  -> less_or_equal(epsilon_0,n0)*.
% 0.36/0.54  626[2:MRR:625.0,10.0] ||  -> .
% 0.36/0.54  627[1:Spt:626.0,195.2] ||  -> less_or_equal(half(epsilon_0),n0)*.
% 0.36/0.54  628[1:Res:627.0,5.0] ||  -> less_or_equal(epsilon_0,n0)*.
% 0.36/0.54  629[1:MRR:628.0,10.0] ||  -> .
% 0.36/0.54  % SZS output end Refutation
% 0.36/0.54  Formulae used in the proof : minimum3 minimum7 minimum9 less_or_equal_sum_of_halves zero_and_half clause_1 clause_2 clause_3 clause_4 clause_5 clause_6 clause_7_2
% 0.36/0.54  
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