%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GEO178+3 : TPTP v8.1.2. Released v4.0.0.
% 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 20:17:19 EDT 2024

% Result   : Theorem 0.13s 0.35s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   32 (   5 unt;   0 def)
%            Number of atoms       :   71 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   65 (  26   ~;  24   |;   8   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   34 (  31   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [X,Y] :
      ( distinct_points(X,Y)
     => ~ apart_point_and_line(X,line_connecting(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X,Y] :
      ( distinct_points(X,Y)
     => ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f36,conjecture,
    ! [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/sandbox/benchmark/theBenchmark.p') ).

fof(f37,negated_conjecture,
    ~ ! [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(negated_conjecture,[status(cth)],[f36]) ).

fof(f50,plain,
    ! [X,Y] :
      ( ~ distinct_points(X,Y)
      | ~ apart_point_and_line(X,line_connecting(X,Y)) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ distinct_points(X0,X1)
      | ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f52,plain,
    ! [X,Y] :
      ( ~ distinct_points(X,Y)
      | ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ~ distinct_points(X0,X1)
      | ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f60,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(X,Y)
      | distinct_points(X,Z)
      | apart_point_and_line(Z,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f61,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(X,Y)
      | ! [Z] :
          ( distinct_points(X,Z)
          | apart_point_and_line(Z,Y) ) ),
    inference(miniscoping,[status(esa)],[f60]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ apart_point_and_line(X0,X1)
      | distinct_points(X0,X2)
      | apart_point_and_line(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f61]) ).

fof(f127,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)],[f37]) ).

fof(f128,plain,
    ( distinct_points(sk0_0,sk0_1)
    & apart_point_and_line(sk0_2,line_connecting(sk0_0,sk0_1))
    & ( ~ distinct_points(sk0_2,sk0_0)
      | ~ distinct_points(sk0_2,sk0_1) ) ),
    inference(skolemization,[status(esa)],[f127]) ).

fof(f129,plain,
    distinct_points(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f128]) ).

fof(f130,plain,
    apart_point_and_line(sk0_2,line_connecting(sk0_0,sk0_1)),
    inference(cnf_transformation,[status(esa)],[f128]) ).

fof(f131,plain,
    ( ~ distinct_points(sk0_2,sk0_0)
    | ~ distinct_points(sk0_2,sk0_1) ),
    inference(cnf_transformation,[status(esa)],[f128]) ).

fof(f138,plain,
    ( spl0_0
  <=> distinct_points(sk0_2,sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f140,plain,
    ( ~ distinct_points(sk0_2,sk0_0)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f138]) ).

fof(f141,plain,
    ( spl0_1
  <=> distinct_points(sk0_2,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f143,plain,
    ( ~ distinct_points(sk0_2,sk0_1)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f141]) ).

fof(f144,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f131,f138,f141]) ).

fof(f149,plain,
    ! [X0] :
      ( distinct_points(sk0_2,X0)
      | apart_point_and_line(X0,line_connecting(sk0_0,sk0_1)) ),
    inference(resolution,[status(thm)],[f62,f130]) ).

fof(f153,plain,
    ( apart_point_and_line(sk0_0,line_connecting(sk0_0,sk0_1))
    | spl0_0 ),
    inference(resolution,[status(thm)],[f140,f149]) ).

fof(f164,plain,
    ( ~ distinct_points(sk0_0,sk0_1)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f153,f51]) ).

fof(f165,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f164,f129]) ).

fof(f166,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f165]) ).

fof(f167,plain,
    ( apart_point_and_line(sk0_1,line_connecting(sk0_0,sk0_1))
    | spl0_1 ),
    inference(resolution,[status(thm)],[f143,f149]) ).

fof(f180,plain,
    ( ~ distinct_points(sk0_0,sk0_1)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f167,f53]) ).

fof(f181,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f180,f129]) ).

fof(f182,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f181]) ).

fof(f183,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f144,f166,f182]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO178+3 : TPTP v8.1.2. Released v4.0.0.
% 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 01:47:14 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.13/0.35  % Refutation found
% 0.13/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.37  % Elapsed time: 0.019781 seconds
% 0.20/0.37  % CPU time: 0.051605 seconds
% 0.20/0.37  % Total memory used: 2.592 MB
% 0.20/0.37  % Net memory used: 2.566 MB
%------------------------------------------------------------------------------