%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GEO178+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   30 (   4 unt;   0 def)
%            Number of atoms       :   68 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   65 (  27   ~;  22   |;   8   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   4 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(f15,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(f16,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)],[f15]) ).

fof(f29,plain,
    ! [X,Y] :
      ( ~ distinct_points(X,Y)
      | ~ apart_point_and_line(X,line_connecting(X,Y)) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ distinct_points(X0,X1)
      | ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f29]) ).

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

fof(f32,plain,
    ! [X0,X1] :
      ( ~ distinct_points(X0,X1)
      | ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f39,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(f40,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(X,Y)
      | ! [Z] :
          ( distinct_points(X,Z)
          | apart_point_and_line(Z,Y) ) ),
    inference(miniscoping,[status(esa)],[f39]) ).

fof(f41,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)],[f40]) ).

fof(f48,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)],[f16]) ).

fof(f49,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)],[f48]) ).

fof(f50,plain,
    distinct_points(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f51,plain,
    apart_point_and_line(sk0_2,line_connecting(sk0_0,sk0_1)),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f52,plain,
    ( ~ distinct_points(sk0_2,sk0_0)
    | ~ distinct_points(sk0_2,sk0_1) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f53,plain,
    ( spl0_0
  <=> distinct_points(sk0_2,sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f56,plain,
    ( spl0_1
  <=> distinct_points(sk0_2,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f59,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f52,f53,f56]) ).

fof(f63,plain,
    ! [X0] :
      ( distinct_points(sk0_2,X0)
      | apart_point_and_line(X0,line_connecting(sk0_0,sk0_1)) ),
    inference(resolution,[status(thm)],[f41,f51]) ).

fof(f75,plain,
    ( spl0_4
  <=> distinct_points(sk0_0,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f77,plain,
    ( ~ distinct_points(sk0_0,sk0_1)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f75]) ).

fof(f98,plain,
    ( distinct_points(sk0_2,sk0_1)
    | ~ distinct_points(sk0_0,sk0_1) ),
    inference(resolution,[status(thm)],[f63,f32]) ).

fof(f99,plain,
    ( spl0_1
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f98,f56,f75]) ).

fof(f100,plain,
    ( distinct_points(sk0_2,sk0_0)
    | ~ distinct_points(sk0_0,sk0_1) ),
    inference(resolution,[status(thm)],[f63,f30]) ).

fof(f101,plain,
    ( spl0_0
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f100,f53,f75]) ).

fof(f103,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f77,f50]) ).

fof(f104,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f103]) ).

fof(f105,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f59,f99,f101,f104]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GEO178+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue Apr 30 01:16:50 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Drodi V3.6.0
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.36  % Elapsed time: 0.016046 seconds
% 0.18/0.36  % CPU time: 0.040075 seconds
% 0.18/0.36  % Total memory used: 2.420 MB
% 0.18/0.36  % Net memory used: 2.404 MB
%------------------------------------------------------------------------------