TSTP Solution File: SWV019-1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWV019-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.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 : Tue Apr 30 20:45:47 EDT 2024

% Result   : Unsatisfiable 0.08s 0.27s
% Output   : CNFRefutation 0.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   65 (  15 unt;   0 def)
%            Number of atoms       :  139 (   5 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  128 (  54   ~;  64   |;   0   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   14 (  12 usr;  11 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   22 (  22   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X1] :
      ( less_than(X1,lower_bound)
      | less_than(upper_bound,X1)
      | in_array_bounds(array,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y] :
      ( ~ less_than(successor(X),successor(Y))
      | less_than(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y,Z] :
      ( ~ less_than(X,Y)
      | ~ less_than(Y,Z)
      | less_than(X,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X] : less_than(X,successor(X)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ( ~ in_array_bounds(array,index_of_maximal)
    | maximal_value = array_value_at(array,index_of_maximal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    less_than(index_of_maximal,an_index),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ~ less_than(an_index,lower_bound),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ~ less_than(upper_bound,an_index),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ~ less_than(index_of_maximal,lower_bound),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    ( ~ in_array_bounds(array,an_index)
    | less_than(successor(an_index),lower_bound)
    | less_than(successor(upper_bound),successor(an_index))
    | less_than(index_of_maximal,lower_bound)
    | ~ less_than(index_of_maximal,successor(an_index))
    | ~ in_array_bounds(array,index_of_maximal)
    | maximal_value != array_value_at(array,index_of_maximal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,plain,
    ! [X0] :
      ( less_than(X0,lower_bound)
      | less_than(upper_bound,X0)
      | in_array_bounds(array,X0) ),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ~ less_than(successor(X0),successor(X1))
      | less_than(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f13,plain,
    ! [X,Z] :
      ( ! [Y] :
          ( ~ less_than(X,Y)
          | ~ less_than(Y,Z) )
      | less_than(X,Z) ),
    inference(miniscoping,[status(esa)],[f3]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ~ less_than(X0,X1)
      | ~ less_than(X1,X2)
      | less_than(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f15,plain,
    ! [X0] : less_than(X0,successor(X0)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f16,plain,
    ( ~ in_array_bounds(array,index_of_maximal)
    | maximal_value = array_value_at(array,index_of_maximal) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f17,plain,
    less_than(index_of_maximal,an_index),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f18,plain,
    ~ less_than(an_index,lower_bound),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f19,plain,
    ~ less_than(upper_bound,an_index),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f20,plain,
    ~ less_than(index_of_maximal,lower_bound),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f21,plain,
    ( ~ in_array_bounds(array,an_index)
    | less_than(successor(an_index),lower_bound)
    | less_than(successor(upper_bound),successor(an_index))
    | less_than(index_of_maximal,lower_bound)
    | ~ less_than(index_of_maximal,successor(an_index))
    | ~ in_array_bounds(array,index_of_maximal)
    | maximal_value != array_value_at(array,index_of_maximal) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f22,plain,
    ( spl0_0
  <=> in_array_bounds(array,index_of_maximal) ),
    introduced(split_symbol_definition) ).

fof(f24,plain,
    ( ~ in_array_bounds(array,index_of_maximal)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f22]) ).

fof(f25,plain,
    ( spl0_1
  <=> maximal_value = array_value_at(array,index_of_maximal) ),
    introduced(split_symbol_definition) ).

fof(f28,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f16,f22,f25]) ).

fof(f29,plain,
    ( spl0_2
  <=> in_array_bounds(array,an_index) ),
    introduced(split_symbol_definition) ).

fof(f31,plain,
    ( ~ in_array_bounds(array,an_index)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f29]) ).

fof(f32,plain,
    ( spl0_3
  <=> less_than(successor(an_index),lower_bound) ),
    introduced(split_symbol_definition) ).

fof(f33,plain,
    ( less_than(successor(an_index),lower_bound)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f32]) ).

fof(f35,plain,
    ( spl0_4
  <=> less_than(successor(upper_bound),successor(an_index)) ),
    introduced(split_symbol_definition) ).

fof(f36,plain,
    ( less_than(successor(upper_bound),successor(an_index))
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f35]) ).

fof(f38,plain,
    ( spl0_5
  <=> less_than(index_of_maximal,lower_bound) ),
    introduced(split_symbol_definition) ).

fof(f39,plain,
    ( less_than(index_of_maximal,lower_bound)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f38]) ).

fof(f41,plain,
    ( spl0_6
  <=> less_than(index_of_maximal,successor(an_index)) ),
    introduced(split_symbol_definition) ).

fof(f43,plain,
    ( ~ less_than(index_of_maximal,successor(an_index))
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f41]) ).

fof(f44,plain,
    ( ~ spl0_2
    | spl0_3
    | spl0_4
    | spl0_5
    | ~ spl0_6
    | ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f21,f29,f32,f35,f38,f41,f22,f25]) ).

fof(f46,plain,
    ! [X0] :
      ( ~ less_than(X0,index_of_maximal)
      | less_than(X0,an_index) ),
    inference(resolution,[status(thm)],[f14,f17]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ less_than(X0,X1)
      | less_than(X0,successor(X1)) ),
    inference(resolution,[status(thm)],[f14,f15]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ less_than(successor(X0),X1)
      | less_than(X0,X1) ),
    inference(resolution,[status(thm)],[f47,f12]) ).

fof(f145,plain,
    ( spl0_7
  <=> less_than(upper_bound,index_of_maximal) ),
    introduced(split_symbol_definition) ).

fof(f146,plain,
    ( less_than(upper_bound,index_of_maximal)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f145]) ).

fof(f148,plain,
    ( less_than(index_of_maximal,lower_bound)
    | less_than(upper_bound,index_of_maximal)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f24,f11]) ).

fof(f149,plain,
    ( spl0_5
    | spl0_7
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f148,f38,f145,f22]) ).

fof(f150,plain,
    ( $false
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f39,f20]) ).

fof(f151,plain,
    ~ spl0_5,
    inference(contradiction_clause,[status(thm)],[f150]) ).

fof(f157,plain,
    ( ~ less_than(index_of_maximal,an_index)
    | spl0_6 ),
    inference(resolution,[status(thm)],[f43,f47]) ).

fof(f158,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f157,f17]) ).

fof(f159,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f158]) ).

fof(f160,plain,
    ( spl0_8
  <=> less_than(an_index,lower_bound) ),
    introduced(split_symbol_definition) ).

fof(f161,plain,
    ( less_than(an_index,lower_bound)
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f160]) ).

fof(f163,plain,
    ( spl0_9
  <=> less_than(upper_bound,an_index) ),
    introduced(split_symbol_definition) ).

fof(f164,plain,
    ( less_than(upper_bound,an_index)
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f163]) ).

fof(f166,plain,
    ( less_than(an_index,lower_bound)
    | less_than(upper_bound,an_index)
    | spl0_2 ),
    inference(resolution,[status(thm)],[f31,f11]) ).

fof(f167,plain,
    ( spl0_8
    | spl0_9
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f166,f160,f163,f29]) ).

fof(f168,plain,
    ( $false
    | ~ spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f164,f19]) ).

fof(f169,plain,
    ~ spl0_9,
    inference(contradiction_clause,[status(thm)],[f168]) ).

fof(f170,plain,
    ( $false
    | ~ spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f161,f18]) ).

fof(f171,plain,
    ~ spl0_8,
    inference(contradiction_clause,[status(thm)],[f170]) ).

fof(f173,plain,
    ( less_than(an_index,lower_bound)
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f33,f48]) ).

fof(f174,plain,
    ( spl0_8
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f173,f160,f32]) ).

fof(f180,plain,
    ( less_than(upper_bound,an_index)
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f36,f12]) ).

fof(f181,plain,
    ( spl0_9
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f180,f163,f35]) ).

fof(f185,plain,
    ( less_than(upper_bound,an_index)
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f146,f46]) ).

fof(f186,plain,
    ( spl0_9
    | ~ spl0_7 ),
    inference(split_clause,[status(thm)],[f185,f163,f145]) ).

fof(f188,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f28,f44,f149,f151,f159,f167,f169,f171,f174,f181,f186]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SWV019-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.26  % Computer : n021.cluster.edu
% 0.08/0.26  % Model    : x86_64 x86_64
% 0.08/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26  % Memory   : 8042.1875MB
% 0.08/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26  % CPULimit : 300
% 0.08/0.26  % WCLimit  : 300
% 0.08/0.26  % DateTime : Tue Apr 30 00:43:40 EDT 2024
% 0.08/0.26  % CPUTime  : 
% 0.08/0.26  % Drodi V3.6.0
% 0.08/0.27  % Refutation found
% 0.08/0.27  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.27  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.27  % Elapsed time: 0.013321 seconds
% 0.08/0.27  % CPU time: 0.032242 seconds
% 0.08/0.27  % Total memory used: 12.931 MB
% 0.08/0.27  % Net memory used: 12.852 MB
%------------------------------------------------------------------------------