TSTP Solution File: PUZ128+2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : PUZ128+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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  : 300s
% DateTime : Fri May  3 02:54:55 EDT 2024

% Result   : Theorem 0.48s 1.14s
% Output   : CNFRefutation 0.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   79 (  40 unt;   0 def)
%            Number of atoms       :  313 (  87 equ)
%            Maximal formula atoms :   32 (   3 avg)
%            Number of connectives :  378 ( 144   ~; 131   |; 101   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   3 usr;   2 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;  10 con; 0-1 aty)
%            Number of variables   :  101 (   0 sgn  40   !;  33   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ? [X0,X1,X2,X3,X4] :
      ( ~ ? [X5] :
            ( 'Thersandros' = X5
            & patricide(X5) )
      & 'Oedipus' = X4
      & patricide(X4)
      & 'Polyneikes' = X3
      & relation(X3,of,'Thersandros')
      & parent(X3)
      & 'Oedipus' = X2
      & relation(X2,of,'Polyneikes')
      & parent(X2)
      & 'Iokaste' = X1
      & relation(X1,of,'Polyneikes')
      & parent(X1)
      & 'Iokaste' = X0
      & relation(X0,of,'Oedipus')
      & parent(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',background) ).

fof(f2,conjecture,
    ? [X0,X1,X2,X3] :
      ( 'Iokaste' = X0
      & relation(X0,of,X1)
      & X1 = X2
      & relation(X2,of,X3)
      & ~ ? [X4] :
            ( X3 = X4
            & patricide(X4) )
      & $true
      & parent(X2)
      & patricide(X1)
      & parent(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).

fof(f3,negated_conjecture,
    ~ ? [X0,X1,X2,X3] :
        ( 'Iokaste' = X0
        & relation(X0,of,X1)
        & X1 = X2
        & relation(X2,of,X3)
        & ~ ? [X4] :
              ( X3 = X4
              & patricide(X4) )
        & $true
        & parent(X2)
        & patricide(X1)
        & parent(X0) ),
    inference(negated_conjecture,[],[f2]) ).

fof(f4,plain,
    ~ ? [X0,X1,X2,X3] :
        ( 'Iokaste' = X0
        & relation(X0,of,X1)
        & X1 = X2
        & relation(X2,of,X3)
        & ~ ? [X4] :
              ( X3 = X4
              & patricide(X4) )
        & parent(X2)
        & patricide(X1)
        & parent(X0) ),
    inference(true_and_false_elimination,[],[f3]) ).

fof(f5,plain,
    ? [X0,X1,X2,X3,X4] :
      ( ! [X5] :
          ( 'Thersandros' != X5
          | ~ patricide(X5) )
      & 'Oedipus' = X4
      & patricide(X4)
      & 'Polyneikes' = X3
      & relation(X3,of,'Thersandros')
      & parent(X3)
      & 'Oedipus' = X2
      & relation(X2,of,'Polyneikes')
      & parent(X2)
      & 'Iokaste' = X1
      & relation(X1,of,'Polyneikes')
      & parent(X1)
      & 'Iokaste' = X0
      & relation(X0,of,'Oedipus')
      & parent(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f6,plain,
    ! [X0,X1,X2,X3] :
      ( 'Iokaste' != X0
      | ~ relation(X0,of,X1)
      | X1 != X2
      | ~ relation(X2,of,X3)
      | ? [X4] :
          ( X3 = X4
          & patricide(X4) )
      | ~ parent(X2)
      | ~ patricide(X1)
      | ~ parent(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f7,plain,
    ( ? [X0,X1,X2,X3,X4] :
        ( ! [X5] :
            ( 'Thersandros' != X5
            | ~ patricide(X5) )
        & 'Oedipus' = X4
        & patricide(X4)
        & 'Polyneikes' = X3
        & relation(X3,of,'Thersandros')
        & parent(X3)
        & 'Oedipus' = X2
        & relation(X2,of,'Polyneikes')
        & parent(X2)
        & 'Iokaste' = X1
        & relation(X1,of,'Polyneikes')
        & parent(X1)
        & 'Iokaste' = X0
        & relation(X0,of,'Oedipus')
        & parent(X0) )
   => ( ! [X5] :
          ( 'Thersandros' != X5
          | ~ patricide(X5) )
      & 'Oedipus' = sK4
      & patricide(sK4)
      & 'Polyneikes' = sK3
      & relation(sK3,of,'Thersandros')
      & parent(sK3)
      & 'Oedipus' = sK2
      & relation(sK2,of,'Polyneikes')
      & parent(sK2)
      & 'Iokaste' = sK1
      & relation(sK1,of,'Polyneikes')
      & parent(sK1)
      & 'Iokaste' = sK0
      & relation(sK0,of,'Oedipus')
      & parent(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ( ! [X5] :
        ( 'Thersandros' != X5
        | ~ patricide(X5) )
    & 'Oedipus' = sK4
    & patricide(sK4)
    & 'Polyneikes' = sK3
    & relation(sK3,of,'Thersandros')
    & parent(sK3)
    & 'Oedipus' = sK2
    & relation(sK2,of,'Polyneikes')
    & parent(sK2)
    & 'Iokaste' = sK1
    & relation(sK1,of,'Polyneikes')
    & parent(sK1)
    & 'Iokaste' = sK0
    & relation(sK0,of,'Oedipus')
    & parent(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f5,f7]) ).

fof(f9,plain,
    ! [X3] :
      ( ? [X4] :
          ( X3 = X4
          & patricide(X4) )
     => ( sK5(X3) = X3
        & patricide(sK5(X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ! [X0,X1,X2,X3] :
      ( 'Iokaste' != X0
      | ~ relation(X0,of,X1)
      | X1 != X2
      | ~ relation(X2,of,X3)
      | ( sK5(X3) = X3
        & patricide(sK5(X3)) )
      | ~ parent(X2)
      | ~ patricide(X1)
      | ~ parent(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f6,f9]) ).

fof(f12,plain,
    relation(sK0,of,'Oedipus'),
    inference(cnf_transformation,[],[f8]) ).

fof(f13,plain,
    'Iokaste' = sK0,
    inference(cnf_transformation,[],[f8]) ).

fof(f14,plain,
    parent(sK1),
    inference(cnf_transformation,[],[f8]) ).

fof(f15,plain,
    relation(sK1,of,'Polyneikes'),
    inference(cnf_transformation,[],[f8]) ).

fof(f16,plain,
    'Iokaste' = sK1,
    inference(cnf_transformation,[],[f8]) ).

fof(f17,plain,
    parent(sK2),
    inference(cnf_transformation,[],[f8]) ).

fof(f18,plain,
    relation(sK2,of,'Polyneikes'),
    inference(cnf_transformation,[],[f8]) ).

fof(f19,plain,
    'Oedipus' = sK2,
    inference(cnf_transformation,[],[f8]) ).

fof(f20,plain,
    parent(sK3),
    inference(cnf_transformation,[],[f8]) ).

fof(f21,plain,
    relation(sK3,of,'Thersandros'),
    inference(cnf_transformation,[],[f8]) ).

fof(f22,plain,
    'Polyneikes' = sK3,
    inference(cnf_transformation,[],[f8]) ).

fof(f23,plain,
    patricide(sK4),
    inference(cnf_transformation,[],[f8]) ).

fof(f24,plain,
    'Oedipus' = sK4,
    inference(cnf_transformation,[],[f8]) ).

fof(f25,plain,
    ! [X5] :
      ( 'Thersandros' != X5
      | ~ patricide(X5) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f26,plain,
    ! [X2,X3,X0,X1] :
      ( 'Iokaste' != X0
      | ~ relation(X0,of,X1)
      | X1 != X2
      | ~ relation(X2,of,X3)
      | patricide(sK5(X3))
      | ~ parent(X2)
      | ~ patricide(X1)
      | ~ parent(X0) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f27,plain,
    ! [X2,X3,X0,X1] :
      ( 'Iokaste' != X0
      | ~ relation(X0,of,X1)
      | X1 != X2
      | ~ relation(X2,of,X3)
      | sK5(X3) = X3
      | ~ parent(X2)
      | ~ patricide(X1)
      | ~ parent(X0) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f28,plain,
    sK2 = sK4,
    inference(definition_unfolding,[],[f19,f24]) ).

fof(f29,plain,
    relation(sK2,of,sK3),
    inference(definition_unfolding,[],[f18,f22]) ).

fof(f30,plain,
    relation(sK1,of,sK3),
    inference(definition_unfolding,[],[f15,f22]) ).

fof(f31,plain,
    sK0 = sK1,
    inference(definition_unfolding,[],[f13,f16]) ).

fof(f32,plain,
    relation(sK0,of,sK4),
    inference(definition_unfolding,[],[f12,f24]) ).

fof(f33,plain,
    ! [X2,X3,X0,X1] :
      ( sK1 != X0
      | ~ relation(X0,of,X1)
      | X1 != X2
      | ~ relation(X2,of,X3)
      | sK5(X3) = X3
      | ~ parent(X2)
      | ~ patricide(X1)
      | ~ parent(X0) ),
    inference(definition_unfolding,[],[f27,f16]) ).

fof(f34,plain,
    ! [X2,X3,X0,X1] :
      ( sK1 != X0
      | ~ relation(X0,of,X1)
      | X1 != X2
      | ~ relation(X2,of,X3)
      | patricide(sK5(X3))
      | ~ parent(X2)
      | ~ patricide(X1)
      | ~ parent(X0) ),
    inference(definition_unfolding,[],[f26,f16]) ).

fof(f35,plain,
    ~ patricide('Thersandros'),
    inference(equality_resolution,[],[f25]) ).

fof(f36,plain,
    ! [X2,X3,X1] :
      ( ~ relation(sK1,of,X1)
      | X1 != X2
      | ~ relation(X2,of,X3)
      | sK5(X3) = X3
      | ~ parent(X2)
      | ~ patricide(X1)
      | ~ parent(sK1) ),
    inference(equality_resolution,[],[f33]) ).

fof(f37,plain,
    ! [X2,X3] :
      ( ~ relation(sK1,of,X2)
      | ~ relation(X2,of,X3)
      | sK5(X3) = X3
      | ~ parent(X2)
      | ~ patricide(X2)
      | ~ parent(sK1) ),
    inference(equality_resolution,[],[f36]) ).

fof(f38,plain,
    ! [X2,X3,X1] :
      ( ~ relation(sK1,of,X1)
      | X1 != X2
      | ~ relation(X2,of,X3)
      | patricide(sK5(X3))
      | ~ parent(X2)
      | ~ patricide(X1)
      | ~ parent(sK1) ),
    inference(equality_resolution,[],[f34]) ).

fof(f39,plain,
    ! [X2,X3] :
      ( ~ relation(sK1,of,X2)
      | ~ relation(X2,of,X3)
      | patricide(sK5(X3))
      | ~ parent(X2)
      | ~ patricide(X2)
      | ~ parent(sK1) ),
    inference(equality_resolution,[],[f38]) ).

cnf(c_49,plain,
    ~ patricide('Thersandros'),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_50,plain,
    patricide(sK4),
    inference(cnf_transformation,[],[f23]) ).

cnf(c_51,plain,
    relation(sK3,of,'Thersandros'),
    inference(cnf_transformation,[],[f21]) ).

cnf(c_52,plain,
    parent(sK3),
    inference(cnf_transformation,[],[f20]) ).

cnf(c_53,plain,
    sK4 = sK2,
    inference(cnf_transformation,[],[f28]) ).

cnf(c_54,plain,
    relation(sK2,of,sK3),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_55,plain,
    parent(sK2),
    inference(cnf_transformation,[],[f17]) ).

cnf(c_56,plain,
    relation(sK1,of,sK3),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_57,plain,
    parent(sK1),
    inference(cnf_transformation,[],[f14]) ).

cnf(c_58,plain,
    sK1 = sK0,
    inference(cnf_transformation,[],[f31]) ).

cnf(c_59,plain,
    relation(sK0,of,sK4),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_61,negated_conjecture,
    ( ~ relation(X0,of,X1)
    | ~ relation(sK1,of,X0)
    | ~ patricide(X0)
    | ~ parent(X0)
    | ~ parent(sK1)
    | sK5(X1) = X1 ),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_62,negated_conjecture,
    ( ~ relation(X0,of,X1)
    | ~ relation(sK1,of,X0)
    | ~ patricide(X0)
    | ~ parent(X0)
    | ~ parent(sK1)
    | patricide(sK5(X1)) ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_65,plain,
    ( ~ parent(X0)
    | ~ patricide(X0)
    | ~ relation(sK1,of,X0)
    | ~ relation(X0,of,X1)
    | patricide(sK5(X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_62,c_57,c_62]) ).

cnf(c_66,negated_conjecture,
    ( ~ relation(X0,of,X1)
    | ~ relation(sK1,of,X0)
    | ~ patricide(X0)
    | ~ parent(X0)
    | patricide(sK5(X1)) ),
    inference(renaming,[status(thm)],[c_65]) ).

cnf(c_68,plain,
    ( ~ parent(X0)
    | ~ patricide(X0)
    | ~ relation(sK1,of,X0)
    | ~ relation(X0,of,X1)
    | sK5(X1) = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_61,c_57,c_61]) ).

cnf(c_69,negated_conjecture,
    ( ~ relation(X0,of,X1)
    | ~ relation(sK1,of,X0)
    | ~ patricide(X0)
    | ~ parent(X0)
    | sK5(X1) = X1 ),
    inference(renaming,[status(thm)],[c_68]) ).

cnf(c_115,plain,
    relation(sK1,of,sK4),
    inference(demodulation,[status(thm)],[c_59,c_58]) ).

cnf(c_117,plain,
    relation(sK4,of,sK3),
    inference(demodulation,[status(thm)],[c_54,c_53]) ).

cnf(c_118,plain,
    parent(sK4),
    inference(demodulation,[status(thm)],[c_55,c_53]) ).

cnf(c_140,plain,
    ( X0 != sK3
    | ~ relation(X0,of,X1)
    | ~ relation(sK1,of,X0)
    | ~ patricide(X0)
    | sK5(X1) = X1 ),
    inference(resolution_lifted,[status(thm)],[c_52,c_69]) ).

cnf(c_141,plain,
    ( ~ relation(sK3,of,X0)
    | ~ relation(sK1,of,sK3)
    | ~ patricide(sK3)
    | sK5(X0) = X0 ),
    inference(unflattening,[status(thm)],[c_140]) ).

cnf(c_143,plain,
    ( ~ relation(sK3,of,X0)
    | ~ patricide(sK3)
    | sK5(X0) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_141,c_56,c_141]) ).

cnf(c_155,plain,
    ( X0 != sK3
    | ~ relation(X0,of,X1)
    | ~ relation(sK1,of,X0)
    | ~ patricide(X0)
    | patricide(sK5(X1)) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_66]) ).

cnf(c_156,plain,
    ( ~ relation(sK3,of,X0)
    | ~ relation(sK1,of,sK3)
    | ~ patricide(sK3)
    | patricide(sK5(X0)) ),
    inference(unflattening,[status(thm)],[c_155]) ).

cnf(c_158,plain,
    ( ~ relation(sK3,of,X0)
    | ~ patricide(sK3)
    | patricide(sK5(X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_156,c_56,c_156]) ).

cnf(c_200,plain,
    ( X0 != sK4
    | ~ relation(X0,of,X1)
    | ~ relation(sK1,of,X0)
    | ~ patricide(X0)
    | sK5(X1) = X1 ),
    inference(resolution_lifted,[status(thm)],[c_69,c_118]) ).

cnf(c_201,plain,
    ( ~ relation(sK4,of,X0)
    | ~ relation(sK1,of,sK4)
    | ~ patricide(sK4)
    | sK5(X0) = X0 ),
    inference(unflattening,[status(thm)],[c_200]) ).

cnf(c_203,plain,
    ( ~ relation(sK4,of,X0)
    | sK5(X0) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_201,c_50,c_115,c_201]) ).

cnf(c_212,plain,
    ( X0 != sK4
    | ~ relation(X0,of,X1)
    | ~ relation(sK1,of,X0)
    | ~ patricide(X0)
    | patricide(sK5(X1)) ),
    inference(resolution_lifted,[status(thm)],[c_66,c_118]) ).

cnf(c_213,plain,
    ( ~ relation(sK4,of,X0)
    | ~ relation(sK1,of,sK4)
    | ~ patricide(sK4)
    | patricide(sK5(X0)) ),
    inference(unflattening,[status(thm)],[c_212]) ).

cnf(c_215,plain,
    ( ~ relation(sK4,of,X0)
    | patricide(sK5(X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_213,c_50,c_115,c_213]) ).

cnf(c_473,plain,
    ( ~ patricide(sK3)
    | sK5('Thersandros') = 'Thersandros' ),
    inference(superposition,[status(thm)],[c_51,c_143]) ).

cnf(c_474,plain,
    ( ~ patricide(sK3)
    | patricide(sK5('Thersandros')) ),
    inference(superposition,[status(thm)],[c_51,c_158]) ).

cnf(c_485,plain,
    sK5(sK3) = sK3,
    inference(superposition,[status(thm)],[c_117,c_203]) ).

cnf(c_486,plain,
    patricide(sK5(sK3)),
    inference(superposition,[status(thm)],[c_117,c_215]) ).

cnf(c_487,plain,
    patricide(sK3),
    inference(light_normalisation,[status(thm)],[c_486,c_485]) ).

cnf(c_502,plain,
    patricide(sK5('Thersandros')),
    inference(forward_subsumption_resolution,[status(thm)],[c_474,c_487]) ).

cnf(c_509,plain,
    sK5('Thersandros') = 'Thersandros',
    inference(forward_subsumption_resolution,[status(thm)],[c_473,c_487]) ).

cnf(c_510,plain,
    patricide('Thersandros'),
    inference(demodulation,[status(thm)],[c_502,c_509]) ).

cnf(c_511,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_510,c_49]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : PUZ128+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n023.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  : 300
% 0.14/0.34  % DateTime : Thu May  2 21:21:24 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.21/0.47  Running first-order theorem proving
% 0.21/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.48/1.14  % SZS status Started for theBenchmark.p
% 0.48/1.14  % SZS status Theorem for theBenchmark.p
% 0.48/1.14  
% 0.48/1.14  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.48/1.14  
% 0.48/1.14  ------  iProver source info
% 0.48/1.14  
% 0.48/1.14  git: date: 2024-05-02 19:28:25 +0000
% 0.48/1.14  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.48/1.14  git: non_committed_changes: false
% 0.48/1.14  
% 0.48/1.14  ------ Parsing...
% 0.48/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.48/1.14  
% 0.48/1.14  ------ Preprocessing... sup_sim: 5  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e 
% 0.48/1.14  
% 0.48/1.14  ------ Preprocessing... gs_s  sp: 2 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.48/1.14  
% 0.48/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.48/1.14  ------ Proving...
% 0.48/1.14  ------ Problem Properties 
% 0.48/1.14  
% 0.48/1.14  
% 0.48/1.14  clauses                                 16
% 0.48/1.14  conjectures                             0
% 0.48/1.14  EPR                                     10
% 0.48/1.14  Horn                                    16
% 0.48/1.14  unary                                   8
% 0.48/1.14  binary                                  2
% 0.48/1.14  lits                                    30
% 0.48/1.14  lits eq                                 5
% 0.48/1.14  fd_pure                                 0
% 0.48/1.14  fd_pseudo                               0
% 0.48/1.14  fd_cond                                 0
% 0.48/1.14  fd_pseudo_cond                          0
% 0.48/1.14  AC symbols                              0
% 0.48/1.14  
% 0.48/1.14  ------ Schedule dynamic 5 is on 
% 0.48/1.14  
% 0.48/1.14  ------ no conjectures: strip conj schedule 
% 0.48/1.14  
% 0.48/1.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.48/1.14  
% 0.48/1.14  
% 0.48/1.14  ------ 
% 0.48/1.14  Current options:
% 0.48/1.14  ------ 
% 0.48/1.14  
% 0.48/1.14  
% 0.48/1.14  
% 0.48/1.14  
% 0.48/1.14  ------ Proving...
% 0.48/1.14  
% 0.48/1.14  
% 0.48/1.14  % SZS status Theorem for theBenchmark.p
% 0.48/1.14  
% 0.48/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.48/1.14  
% 0.48/1.14  
%------------------------------------------------------------------------------