%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GEO209+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n024.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 12:08:18 EDT 2023

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   32 (   8 unt;   0 def)
%            Number of atoms       :   90 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  100 (  42   ~;  29   |;  23   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   42 (;  34   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( convergent_lines(X,Z)
        | convergent_lines(Y,Z) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [X,Y,Z] :
      ( distinct_lines(Y,Z)
     => ( apart_point_and_line(X,Y)
        | apart_point_and_line(X,Z)
        | convergent_lines(Y,Z) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,conjecture,
    ! [A,L,M,N] :
      ( ( apart_point_and_line(A,L)
        & ~ apart_point_and_line(A,M)
        & ~ apart_point_and_line(A,N)
        & ~ convergent_lines(M,L)
        & ~ convergent_lines(N,L) )
     => ~ distinct_lines(M,N) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,negated_conjecture,
    ~ ! [A,L,M,N] :
        ( ( apart_point_and_line(A,L)
          & ~ apart_point_and_line(A,M)
          & ~ apart_point_and_line(A,N)
          & ~ convergent_lines(M,L)
          & ~ convergent_lines(N,L) )
       => ~ distinct_lines(M,N) ),
    inference(negated_conjecture,[status(cth)],[f18]) ).

fof(f29,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | convergent_lines(Y,Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f30,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | ! [Z] :
          ( convergent_lines(X,Z)
          | convergent_lines(Y,Z) ) ),
    inference(miniscoping,[status(esa)],[f29]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,X2)
      | convergent_lines(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f53,plain,
    ! [X,Y,Z] :
      ( ~ distinct_lines(Y,Z)
      | apart_point_and_line(X,Y)
      | apart_point_and_line(X,Z)
      | convergent_lines(Y,Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f17]) ).

fof(f54,plain,
    ! [Y,Z] :
      ( ~ distinct_lines(Y,Z)
      | ! [X] :
          ( apart_point_and_line(X,Y)
          | apart_point_and_line(X,Z) )
      | convergent_lines(Y,Z) ),
    inference(miniscoping,[status(esa)],[f53]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( ~ distinct_lines(X0,X1)
      | apart_point_and_line(X2,X0)
      | apart_point_and_line(X2,X1)
      | convergent_lines(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f56,plain,
    ? [A,L,M,N] :
      ( apart_point_and_line(A,L)
      & ~ apart_point_and_line(A,M)
      & ~ apart_point_and_line(A,N)
      & ~ convergent_lines(M,L)
      & ~ convergent_lines(N,L)
      & distinct_lines(M,N) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f57,plain,
    ? [M,N] :
      ( ? [L] :
          ( ? [A] :
              ( apart_point_and_line(A,L)
              & ~ apart_point_and_line(A,M)
              & ~ apart_point_and_line(A,N) )
          & ~ convergent_lines(M,L)
          & ~ convergent_lines(N,L) )
      & distinct_lines(M,N) ),
    inference(miniscoping,[status(esa)],[f56]) ).

fof(f58,plain,
    ( apart_point_and_line(sk0_3,sk0_2)
    & ~ apart_point_and_line(sk0_3,sk0_0)
    & ~ apart_point_and_line(sk0_3,sk0_1)
    & ~ convergent_lines(sk0_0,sk0_2)
    & ~ convergent_lines(sk0_1,sk0_2)
    & distinct_lines(sk0_0,sk0_1) ),
    inference(skolemization,[status(esa)],[f57]) ).

fof(f60,plain,
    ~ apart_point_and_line(sk0_3,sk0_0),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f61,plain,
    ~ apart_point_and_line(sk0_3,sk0_1),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f62,plain,
    ~ convergent_lines(sk0_0,sk0_2),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f63,plain,
    ~ convergent_lines(sk0_1,sk0_2),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f64,plain,
    distinct_lines(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f71,plain,
    ! [X0] :
      ( ~ distinct_lines(X0,sk0_1)
      | apart_point_and_line(sk0_3,X0)
      | convergent_lines(X0,sk0_1) ),
    inference(resolution,[status(thm)],[f55,f61]) ).

fof(f82,plain,
    ( spl0_2
  <=> distinct_lines(sk0_0,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f84,plain,
    ( ~ distinct_lines(sk0_0,sk0_1)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f82]) ).

fof(f85,plain,
    ( spl0_3
  <=> convergent_lines(sk0_0,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f86,plain,
    ( convergent_lines(sk0_0,sk0_1)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f85]) ).

fof(f88,plain,
    ( ~ distinct_lines(sk0_0,sk0_1)
    | convergent_lines(sk0_0,sk0_1) ),
    inference(resolution,[status(thm)],[f71,f60]) ).

fof(f89,plain,
    ( ~ spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f88,f82,f85]) ).

fof(f91,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f84,f64]) ).

fof(f92,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f91]) ).

fof(f168,plain,
    ! [X0] :
      ( convergent_lines(sk0_0,X0)
      | convergent_lines(sk0_1,X0)
      | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f86,f31]) ).

fof(f186,plain,
    ( convergent_lines(sk0_0,sk0_2)
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f168,f63]) ).

fof(f187,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f186,f62]) ).

fof(f188,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f187]) ).

fof(f189,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f89,f92,f188]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO209+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n024.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 May 30 12:04:18 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 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
% 0.13/0.37  % Elapsed time: 0.020617 seconds
% 0.13/0.37  % CPU time: 0.040111 seconds
% 0.13/0.37  % Memory used: 1.872 MB
%------------------------------------------------------------------------------