TSTP Solution File: GEO225+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GEO225+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n025.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 : Wed May 31 12:08:25 EDT 2023

% Result   : Theorem 0.11s 0.34s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   24 (   6 unt;   0 def)
%            Number of atoms       :   70 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   70 (  24   ~;  18   |;  21   &)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   2 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   38 (;  32   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X] : ~ distinct_points(X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X,Y,Z] :
      ( distinct_points(X,Y)
     => ( apart_point_and_line(Z,line_connecting(X,Y))
       => ( distinct_points(Z,X)
          & distinct_points(Z,Y) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,conjecture,
    ! [A,B] :
      ( ( point(A)
        & point(B)
        & distinct_points(A,B) )
     => ? [X] :
          ( line(X)
         => ( ~ apart_point_and_line(A,X)
            & ~ apart_point_and_line(B,X) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    ~ ! [A,B] :
        ( ( point(A)
          & point(B)
          & distinct_points(A,B) )
       => ? [X] :
            ( line(X)
           => ( ~ apart_point_and_line(A,X)
              & ~ apart_point_and_line(B,X) ) ) ),
    inference(negated_conjecture,[status(cth)],[f17]) ).

fof(f19,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f31,plain,
    ! [X,Y,Z] :
      ( ~ distinct_points(X,Y)
      | ~ apart_point_and_line(Z,line_connecting(X,Y))
      | ( distinct_points(Z,X)
        & distinct_points(Z,Y) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f32,plain,
    ! [X,Y] :
      ( ~ distinct_points(X,Y)
      | ! [Z] :
          ( ~ apart_point_and_line(Z,line_connecting(X,Y))
          | ( distinct_points(Z,X)
            & distinct_points(Z,Y) ) ) ),
    inference(miniscoping,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ~ distinct_points(X0,X1)
      | ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | distinct_points(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ~ distinct_points(X0,X1)
      | ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | distinct_points(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f57,plain,
    ? [A,B] :
      ( point(A)
      & point(B)
      & distinct_points(A,B)
      & ! [X] :
          ( line(X)
          & ( apart_point_and_line(A,X)
            | apart_point_and_line(B,X) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f58,plain,
    ? [A,B] :
      ( point(A)
      & point(B)
      & distinct_points(A,B)
      & ! [X] : line(X)
      & ! [X] :
          ( apart_point_and_line(A,X)
          | apart_point_and_line(B,X) ) ),
    inference(miniscoping,[status(esa)],[f57]) ).

fof(f59,plain,
    ( point(sk0_0)
    & point(sk0_1)
    & distinct_points(sk0_0,sk0_1)
    & ! [X] : line(X)
    & ! [X] :
        ( apart_point_and_line(sk0_0,X)
        | apart_point_and_line(sk0_1,X) ) ),
    inference(skolemization,[status(esa)],[f58]) ).

fof(f62,plain,
    distinct_points(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f64,plain,
    ! [X0] :
      ( apart_point_and_line(sk0_0,X0)
      | apart_point_and_line(sk0_1,X0) ),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ~ distinct_points(X0,X1)
      | ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
    inference(resolution,[status(thm)],[f33,f19]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ~ distinct_points(X0,X1)
      | ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
    inference(resolution,[status(thm)],[f34,f19]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ distinct_points(X0,sk0_1)
      | apart_point_and_line(sk0_0,line_connecting(X0,sk0_1)) ),
    inference(resolution,[status(thm)],[f75,f64]) ).

fof(f84,plain,
    ( spl0_1
  <=> distinct_points(sk0_0,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f86,plain,
    ( ~ distinct_points(sk0_0,sk0_1)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f84]) ).

fof(f87,plain,
    ( ~ distinct_points(sk0_0,sk0_1)
    | ~ distinct_points(sk0_0,sk0_1) ),
    inference(resolution,[status(thm)],[f81,f71]) ).

fof(f88,plain,
    ~ spl0_1,
    inference(split_clause,[status(thm)],[f87,f84]) ).

fof(f89,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f86,f62]) ).

fof(f90,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f89]) ).

fof(f91,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f88,f90]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : GEO225+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32  % Computer : n025.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Tue May 30 12:10:27 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.11/0.33  % Drodi V3.5.1
% 0.11/0.34  % Refutation found
% 0.11/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.56  % Elapsed time: 0.014286 seconds
% 0.18/0.56  % CPU time: 0.015246 seconds
% 0.18/0.56  % Memory used: 526.333 KB
%------------------------------------------------------------------------------