%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GEO172+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.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 20:17:16 EDT 2024

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   46 (  11 unt;   0 def)
%            Number of atoms       :  122 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  130 (  54   ~;  53   |;  13   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   52 (  49   !;   3   ?)

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

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/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y,U,V] :
      ( ( distinct_points(X,Y)
        & distinct_lines(U,V) )
     => ( apart_point_and_line(X,U)
        | apart_point_and_line(X,V)
        | apart_point_and_line(Y,U)
        | apart_point_and_line(Y,V) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => distinct_lines(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,conjecture,
    ! [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/sandbox/benchmark/theBenchmark.p') ).

fof(f14,negated_conjecture,
    ~ ! [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(negated_conjecture,[status(cth)],[f13]) ).

fof(f15,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

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(f35,plain,
    ! [X,Y,U,V] :
      ( ~ distinct_points(X,Y)
      | ~ distinct_lines(U,V)
      | apart_point_and_line(X,U)
      | apart_point_and_line(X,V)
      | apart_point_and_line(Y,U)
      | apart_point_and_line(Y,V) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f36,plain,
    ! [X0,X1,X2,X3] :
      ( ~ distinct_points(X0,X1)
      | ~ distinct_lines(X2,X3)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f35]) ).

fof(f43,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | distinct_lines(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | distinct_lines(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f45,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)],[f14]) ).

fof(f46,plain,
    ( convergent_lines(sk0_0,sk0_1)
    & ~ apart_point_and_line(sk0_2,sk0_0)
    & ~ apart_point_and_line(sk0_2,sk0_1)
    & distinct_points(sk0_2,intersection_point(sk0_0,sk0_1)) ),
    inference(skolemization,[status(esa)],[f45]) ).

fof(f47,plain,
    convergent_lines(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f48,plain,
    ~ apart_point_and_line(sk0_2,sk0_0),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f49,plain,
    ~ apart_point_and_line(sk0_2,sk0_1),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f50,plain,
    distinct_points(sk0_2,intersection_point(sk0_0,sk0_1)),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f66,plain,
    ! [X0,X1,X2,X3] :
      ( ~ distinct_points(X0,X1)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X1,X3)
      | ~ convergent_lines(X2,X3) ),
    inference(resolution,[status(thm)],[f36,f44]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ distinct_points(X0,X1)
      | apart_point_and_line(X0,sk0_0)
      | apart_point_and_line(X0,sk0_1)
      | apart_point_and_line(X1,sk0_0)
      | apart_point_and_line(X1,sk0_1) ),
    inference(resolution,[status(thm)],[f66,f47]) ).

fof(f73,plain,
    ( spl0_0
  <=> apart_point_and_line(sk0_2,sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f74,plain,
    ( apart_point_and_line(sk0_2,sk0_0)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f73]) ).

fof(f76,plain,
    ( spl0_1
  <=> apart_point_and_line(sk0_2,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f77,plain,
    ( apart_point_and_line(sk0_2,sk0_1)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f76]) ).

fof(f79,plain,
    ( spl0_2
  <=> apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f80,plain,
    ( apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_0)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f79]) ).

fof(f82,plain,
    ( spl0_3
  <=> apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f83,plain,
    ( apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_1)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f82]) ).

fof(f85,plain,
    ( apart_point_and_line(sk0_2,sk0_0)
    | apart_point_and_line(sk0_2,sk0_1)
    | apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_0)
    | apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_1) ),
    inference(resolution,[status(thm)],[f67,f50]) ).

fof(f86,plain,
    ( spl0_0
    | spl0_1
    | spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f85,f73,f76,f79,f82]) ).

fof(f141,plain,
    ! [X0] :
      ( ~ convergent_lines(X0,sk0_1)
      | distinct_points(intersection_point(sk0_0,sk0_1),intersection_point(X0,sk0_1))
      | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f83,f34]) ).

fof(f157,plain,
    ( ~ convergent_lines(sk0_0,sk0_1)
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f141,f15]) ).

fof(f158,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f157,f47]) ).

fof(f159,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f158]) ).

fof(f162,plain,
    ! [X0] :
      ( ~ convergent_lines(sk0_0,X0)
      | distinct_points(intersection_point(sk0_0,sk0_1),intersection_point(sk0_0,X0))
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f80,f33]) ).

fof(f182,plain,
    ( ~ convergent_lines(sk0_0,sk0_1)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f162,f15]) ).

fof(f183,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f182,f47]) ).

fof(f184,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f183]) ).

fof(f185,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f74,f48]) ).

fof(f186,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f185]) ).

fof(f187,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f77,f49]) ).

fof(f188,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f187]) ).

fof(f189,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f86,f159,f184,f186,f188]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO172+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Apr 30 01:53:14 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.13/0.36  % Refutation found
% 0.13/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.38  % Elapsed time: 0.030201 seconds
% 0.19/0.38  % CPU time: 0.135914 seconds
% 0.19/0.38  % Total memory used: 5.365 MB
% 0.19/0.38  % Net memory used: 5.194 MB
%------------------------------------------------------------------------------