%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GEO185+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n013.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 12:08:07 EDT 2023

% Result   : Theorem 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   25 (   4 unt;   0 def)
%            Number of atoms       :   69 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   74 (  30   ~;  20   |;  17   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   4 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   31 (;  23   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( ( apart_point_and_line(Z,X)
          | apart_point_and_line(Z,Y) )
       => distinct_points(Z,intersection_point(X,Y)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,conjecture,
    ! [X,Y,U,V] :
      ( ( distinct_points(X,Y)
        & convergent_lines(U,V)
        & ~ distinct_points(X,intersection_point(U,V)) )
     => ( ~ apart_point_and_line(X,U)
        & ~ apart_point_and_line(X,V) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,negated_conjecture,
    ~ ! [X,Y,U,V] :
        ( ( distinct_points(X,Y)
          & convergent_lines(U,V)
          & ~ distinct_points(X,intersection_point(U,V)) )
       => ( ~ apart_point_and_line(X,U)
          & ~ apart_point_and_line(X,V) ) ),
    inference(negated_conjecture,[status(cth)],[f13]) ).

fof(f31,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | ( ~ apart_point_and_line(Z,X)
        & ~ apart_point_and_line(Z,Y) )
      | distinct_points(Z,intersection_point(X,Y)) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

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

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

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

fof(f45,plain,
    ? [X,Y,U,V] :
      ( distinct_points(X,Y)
      & convergent_lines(U,V)
      & ~ distinct_points(X,intersection_point(U,V))
      & ( apart_point_and_line(X,U)
        | apart_point_and_line(X,V) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f46,plain,
    ? [X,U,V] :
      ( ? [Y] : distinct_points(X,Y)
      & convergent_lines(U,V)
      & ~ distinct_points(X,intersection_point(U,V))
      & ( apart_point_and_line(X,U)
        | apart_point_and_line(X,V) ) ),
    inference(miniscoping,[status(esa)],[f45]) ).

fof(f47,plain,
    ( distinct_points(sk0_0,sk0_3)
    & convergent_lines(sk0_1,sk0_2)
    & ~ distinct_points(sk0_0,intersection_point(sk0_1,sk0_2))
    & ( apart_point_and_line(sk0_0,sk0_1)
      | apart_point_and_line(sk0_0,sk0_2) ) ),
    inference(skolemization,[status(esa)],[f46]) ).

fof(f49,plain,
    convergent_lines(sk0_1,sk0_2),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f50,plain,
    ~ distinct_points(sk0_0,intersection_point(sk0_1,sk0_2)),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f51,plain,
    ( apart_point_and_line(sk0_0,sk0_1)
    | apart_point_and_line(sk0_0,sk0_2) ),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f52,plain,
    ( spl0_0
  <=> apart_point_and_line(sk0_0,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f55,plain,
    ( spl0_1
  <=> apart_point_and_line(sk0_0,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f58,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f51,f52,f55]) ).

fof(f78,plain,
    ( spl0_2
  <=> convergent_lines(sk0_1,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f80,plain,
    ( ~ convergent_lines(sk0_1,sk0_2)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f78]) ).

fof(f81,plain,
    ( ~ convergent_lines(sk0_1,sk0_2)
    | ~ apart_point_and_line(sk0_0,sk0_1) ),
    inference(resolution,[status(thm)],[f33,f50]) ).

fof(f82,plain,
    ( ~ spl0_2
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f81,f78,f52]) ).

fof(f85,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f80,f49]) ).

fof(f86,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f85]) ).

fof(f87,plain,
    ( ~ convergent_lines(sk0_1,sk0_2)
    | ~ apart_point_and_line(sk0_0,sk0_2) ),
    inference(resolution,[status(thm)],[f34,f50]) ).

fof(f88,plain,
    ( ~ spl0_2
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f87,f78,f55]) ).

fof(f91,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f58,f82,f86,f88]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO185+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.32  % Computer : n013.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Tue May 30 11:59:20 EDT 2023
% 0.12/0.32  % CPUTime  : 
% 0.12/0.33  % Drodi V3.5.1
% 0.12/0.34  % Refutation found
% 0.12/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.34  % Elapsed time: 0.020974 seconds
% 0.12/0.35  % CPU time: 0.055636 seconds
% 0.12/0.35  % Memory used: 2.404 MB
%------------------------------------------------------------------------------