%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GEO183+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.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 20:17:21 EDT 2024

% Result   : Theorem 0.14s 0.37s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   46 (  10 unt;   0 def)
%            Number of atoms       :  114 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  102 (  34   ~;  43   |;  17   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   79 (  71   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X] : ~ convergent_lines(X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f13,axiom,
    ! [X,Y,Z] :
      ( apart_point_and_line(X,Y)
     => ( distinct_lines(Y,Z)
        | apart_point_and_line(X,Z) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [X,Y] :
      ( distinct_lines(X,Y)
     => convergent_lines(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f34,axiom,
    ! [X,Y] :
      ( incident_point_and_line(X,Y)
    <=> ~ apart_point_and_line(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f36,conjecture,
    ! [X,Y,U,V] :
      ( ( distinct_points(X,Y)
        & convergent_lines(U,V)
        & equal_lines(U,line_connecting(X,Y)) )
     => ( incident_point_and_line(X,U)
        & incident_point_and_line(Y,U) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,negated_conjecture,
    ~ ! [X,Y,U,V] :
        ( ( distinct_points(X,Y)
          & convergent_lines(U,V)
          & equal_lines(U,line_connecting(X,Y)) )
       => ( incident_point_and_line(X,U)
          & incident_point_and_line(Y,U) ) ),
    inference(negated_conjecture,[status(cth)],[f36]) ).

fof(f40,plain,
    ! [X0] : ~ convergent_lines(X0,X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f47,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | convergent_lines(Y,Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f48,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | ! [Z] :
          ( convergent_lines(X,Z)
          | convergent_lines(Y,Z) ) ),
    inference(miniscoping,[status(esa)],[f47]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,X2)
      | convergent_lines(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f63,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(X,Y)
      | distinct_lines(Y,Z)
      | apart_point_and_line(X,Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f64,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(X,Y)
      | ! [Z] :
          ( distinct_lines(Y,Z)
          | apart_point_and_line(X,Z) ) ),
    inference(miniscoping,[status(esa)],[f63]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( ~ apart_point_and_line(X0,X1)
      | distinct_lines(X1,X2)
      | apart_point_and_line(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f69,plain,
    ! [X,Y] :
      ( ~ distinct_lines(X,Y)
      | convergent_lines(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ distinct_lines(X0,X1)
      | convergent_lines(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f71,plain,
    ! [X0,X1] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f72,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f119,plain,
    ! [X,Y] :
      ( ( ~ incident_point_and_line(X,Y)
        | ~ apart_point_and_line(X,Y) )
      & ( incident_point_and_line(X,Y)
        | apart_point_and_line(X,Y) ) ),
    inference(NNF_transformation,[status(esa)],[f34]) ).

fof(f120,plain,
    ( ! [X,Y] :
        ( ~ incident_point_and_line(X,Y)
        | ~ apart_point_and_line(X,Y) )
    & ! [X,Y] :
        ( incident_point_and_line(X,Y)
        | apart_point_and_line(X,Y) ) ),
    inference(miniscoping,[status(esa)],[f119]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( incident_point_and_line(X0,X1)
      | apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f120]) ).

fof(f127,plain,
    ? [X,Y,U,V] :
      ( distinct_points(X,Y)
      & convergent_lines(U,V)
      & equal_lines(U,line_connecting(X,Y))
      & ( ~ incident_point_and_line(X,U)
        | ~ incident_point_and_line(Y,U) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f128,plain,
    ? [X,Y,U] :
      ( distinct_points(X,Y)
      & ? [V] : convergent_lines(U,V)
      & equal_lines(U,line_connecting(X,Y))
      & ( ~ incident_point_and_line(X,U)
        | ~ incident_point_and_line(Y,U) ) ),
    inference(miniscoping,[status(esa)],[f127]) ).

fof(f129,plain,
    ( distinct_points(sk0_0,sk0_1)
    & convergent_lines(sk0_2,sk0_3)
    & equal_lines(sk0_2,line_connecting(sk0_0,sk0_1))
    & ( ~ incident_point_and_line(sk0_0,sk0_2)
      | ~ incident_point_and_line(sk0_1,sk0_2) ) ),
    inference(skolemization,[status(esa)],[f128]) ).

fof(f133,plain,
    ( ~ incident_point_and_line(sk0_0,sk0_2)
    | ~ incident_point_and_line(sk0_1,sk0_2) ),
    inference(cnf_transformation,[status(esa)],[f129]) ).

fof(f140,plain,
    ( spl0_0
  <=> incident_point_and_line(sk0_0,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f142,plain,
    ( ~ incident_point_and_line(sk0_0,sk0_2)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f140]) ).

fof(f143,plain,
    ( spl0_1
  <=> incident_point_and_line(sk0_1,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f145,plain,
    ( ~ incident_point_and_line(sk0_1,sk0_2)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f143]) ).

fof(f146,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f133,f140,f143]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X1,X0) ),
    inference(resolution,[status(thm)],[f49,f40]) ).

fof(f170,plain,
    ! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
    inference(resolution,[status(thm)],[f156,f71]) ).

fof(f295,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X0,X1)
      | apart_point_and_line(X2,X1)
      | incident_point_and_line(X2,X0) ),
    inference(resolution,[status(thm)],[f65,f122]) ).

fof(f302,plain,
    ! [X0] :
      ( distinct_lines(sk0_2,X0)
      | apart_point_and_line(sk0_0,X0)
      | spl0_0 ),
    inference(resolution,[status(thm)],[f295,f142]) ).

fof(f318,plain,
    ! [X0] :
      ( apart_point_and_line(sk0_0,X0)
      | convergent_lines(sk0_2,X0)
      | spl0_0 ),
    inference(resolution,[status(thm)],[f302,f70]) ).

fof(f326,plain,
    ! [X0] :
      ( apart_point_and_line(sk0_0,parallel_through_point(sk0_2,X0))
      | spl0_0 ),
    inference(resolution,[status(thm)],[f318,f170]) ).

fof(f329,plain,
    ( $false
    | spl0_0 ),
    inference(resolution,[status(thm)],[f326,f72]) ).

fof(f330,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f329]) ).

fof(f331,plain,
    ! [X0] :
      ( distinct_lines(sk0_2,X0)
      | apart_point_and_line(sk0_1,X0)
      | spl0_1 ),
    inference(resolution,[status(thm)],[f145,f295]) ).

fof(f335,plain,
    ! [X0] :
      ( apart_point_and_line(sk0_1,X0)
      | convergent_lines(sk0_2,X0)
      | spl0_1 ),
    inference(resolution,[status(thm)],[f331,f70]) ).

fof(f343,plain,
    ! [X0] :
      ( apart_point_and_line(sk0_1,parallel_through_point(sk0_2,X0))
      | spl0_1 ),
    inference(resolution,[status(thm)],[f335,f170]) ).

fof(f346,plain,
    ( $false
    | spl0_1 ),
    inference(resolution,[status(thm)],[f343,f72]) ).

fof(f347,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f346]) ).

fof(f348,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f146,f330,f347]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GEO183+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Tue Apr 30 01:41:55 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 0.14/0.37  % Refutation found
% 0.14/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.39  % Elapsed time: 0.028881 seconds
% 0.14/0.39  % CPU time: 0.110664 seconds
% 0.14/0.39  % Total memory used: 4.799 MB
% 0.14/0.39  % Net memory used: 4.685 MB
%------------------------------------------------------------------------------