TSTP Solution File: GEO196+3 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GEO196+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n032.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 12:08:13 EDT 2023

% Result   : Theorem 3.01s 0.79s
% Output   : CNFRefutation 3.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   56 (  12 unt;   0 def)
%            Number of atoms       :  137 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  123 (  42   ~;  55   |;  18   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  107 (; 103   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X] : ~ convergent_lines(X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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(f13,axiom,
    ! [X,Y,Z] :
      ( apart_point_and_line(X,Y)
     => ( distinct_lines(Y,Z)
        | apart_point_and_line(X,Z) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [X,Y] :
      ( distinct_lines(X,Y)
     => convergent_lines(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f34,axiom,
    ! [X,Y] :
      ( incident_point_and_line(X,Y)
    <=> ~ apart_point_and_line(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f36,conjecture,
    ! [X,Y,U,V] :
      ( ( convergent_lines(X,Y)
        & convergent_lines(U,V)
        & incident_point_and_line(intersection_point(X,Y),U)
        & incident_point_and_line(intersection_point(X,Y),V) )
     => ( incident_point_and_line(intersection_point(U,V),X)
        & incident_point_and_line(intersection_point(U,V),Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f37,negated_conjecture,
    ~ ! [X,Y,U,V] :
        ( ( convergent_lines(X,Y)
          & convergent_lines(U,V)
          & incident_point_and_line(intersection_point(X,Y),U)
          & incident_point_and_line(intersection_point(X,Y),V) )
       => ( incident_point_and_line(intersection_point(U,V),X)
          & incident_point_and_line(intersection_point(U,V),Y) ) ),
    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] :
      ( convergent_lines(X,Y)
      & convergent_lines(U,V)
      & incident_point_and_line(intersection_point(X,Y),U)
      & incident_point_and_line(intersection_point(X,Y),V)
      & ( ~ incident_point_and_line(intersection_point(U,V),X)
        | ~ incident_point_and_line(intersection_point(U,V),Y) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f128,plain,
    ( convergent_lines(sk0_0,sk0_1)
    & convergent_lines(sk0_2,sk0_3)
    & incident_point_and_line(intersection_point(sk0_0,sk0_1),sk0_2)
    & incident_point_and_line(intersection_point(sk0_0,sk0_1),sk0_3)
    & ( ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_0)
      | ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_1) ) ),
    inference(skolemization,[status(esa)],[f127]) ).

fof(f133,plain,
    ( ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_0)
    | ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_1) ),
    inference(cnf_transformation,[status(esa)],[f128]) ).

fof(f140,plain,
    ( spl0_0
  <=> incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f142,plain,
    ( ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_0)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f140]) ).

fof(f143,plain,
    ( spl0_1
  <=> incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f145,plain,
    ( ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_1)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f143]) ).

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

fof(f147,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,parallel_through_point(X1,X2))
      | convergent_lines(X0,X1) ),
    inference(resolution,[status(thm)],[f71,f49]) ).

fof(f148,plain,
    ! [X0,X1,X2,X3] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(X2,X0)
      | convergent_lines(X2,parallel_through_point(X1,X3)) ),
    inference(resolution,[status(thm)],[f147,f49]) ).

fof(f151,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(parallel_through_point(X1,X2),X0) ),
    inference(resolution,[status(thm)],[f148,f40]) ).

fof(f153,plain,
    ! [X0,X1,X2,X3] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(X2,parallel_through_point(X1,X3))
      | convergent_lines(X2,X0) ),
    inference(resolution,[status(thm)],[f151,f49]) ).

fof(f156,plain,
    ! [X0,X1,X2,X3] :
      ( convergent_lines(X0,X1)
      | convergent_lines(X2,X0)
      | convergent_lines(X3,X1)
      | ~ convergent_lines(X2,X3) ),
    inference(resolution,[status(thm)],[f153,f148]) ).

fof(f170,plain,
    ( apart_point_and_line(intersection_point(sk0_2,sk0_3),sk0_0)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f142,f122]) ).

fof(f202,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
      | convergent_lines(X2,X0)
      | ~ convergent_lines(X2,X1) ),
    inference(resolution,[status(thm)],[f156,f40]) ).

fof(f354,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(parallel_through_point(X0,X2),X1) ),
    inference(resolution,[status(thm)],[f202,f71]) ).

fof(f362,plain,
    ! [X0,X1,X2] : ~ convergent_lines(parallel_through_point(parallel_through_point(X0,X1),X2),X0),
    inference(resolution,[status(thm)],[f354,f71]) ).

fof(f374,plain,
    ! [X0,X1,X2,X3] :
      ( ~ convergent_lines(X0,parallel_through_point(parallel_through_point(X1,X2),X3))
      | convergent_lines(X0,X1) ),
    inference(resolution,[status(thm)],[f362,f49]) ).

fof(f426,plain,
    ! [X0,X1,X2] : ~ convergent_lines(X0,parallel_through_point(parallel_through_point(X0,X1),X2)),
    inference(resolution,[status(thm)],[f374,f40]) ).

fof(f472,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,parallel_through_point(X1,X2))
      | ~ convergent_lines(X1,X0) ),
    inference(resolution,[status(thm)],[f426,f148]) ).

fof(f495,plain,
    ! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
    inference(resolution,[status(thm)],[f472,f40]) ).

fof(f610,plain,
    ! [X0] :
      ( distinct_lines(sk0_0,X0)
      | apart_point_and_line(intersection_point(sk0_2,sk0_3),X0)
      | spl0_0 ),
    inference(resolution,[status(thm)],[f65,f170]) ).

fof(f618,plain,
    ! [X0] :
      ( apart_point_and_line(intersection_point(sk0_2,sk0_3),X0)
      | convergent_lines(sk0_0,X0)
      | spl0_0 ),
    inference(resolution,[status(thm)],[f610,f70]) ).

fof(f623,plain,
    ! [X0] :
      ( apart_point_and_line(intersection_point(sk0_2,sk0_3),parallel_through_point(sk0_0,X0))
      | spl0_0 ),
    inference(resolution,[status(thm)],[f618,f495]) ).

fof(f628,plain,
    ( $false
    | spl0_0 ),
    inference(resolution,[status(thm)],[f623,f72]) ).

fof(f629,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f628]) ).

fof(f630,plain,
    ( apart_point_and_line(intersection_point(sk0_2,sk0_3),sk0_1)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f145,f122]) ).

fof(f631,plain,
    ! [X0] :
      ( distinct_lines(sk0_1,X0)
      | apart_point_and_line(intersection_point(sk0_2,sk0_3),X0)
      | spl0_1 ),
    inference(resolution,[status(thm)],[f630,f65]) ).

fof(f635,plain,
    ! [X0] :
      ( apart_point_and_line(intersection_point(sk0_2,sk0_3),X0)
      | convergent_lines(sk0_1,X0)
      | spl0_1 ),
    inference(resolution,[status(thm)],[f631,f70]) ).

fof(f640,plain,
    ! [X0] :
      ( apart_point_and_line(intersection_point(sk0_2,sk0_3),parallel_through_point(sk0_1,X0))
      | spl0_1 ),
    inference(resolution,[status(thm)],[f635,f495]) ).

fof(f645,plain,
    ( $false
    | spl0_1 ),
    inference(resolution,[status(thm)],[f640,f72]) ).

fof(f646,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f645]) ).

fof(f647,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f146,f629,f646]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : GEO196+3 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Tue May 30 12:03:31 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.09/0.30  % Drodi V3.5.1
% 3.01/0.79  % Refutation found
% 3.01/0.79  % SZS status Theorem for theBenchmark: Theorem is valid
% 3.01/0.79  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.01/0.80  % Elapsed time: 0.502430 seconds
% 3.01/0.80  % CPU time: 3.376402 seconds
% 3.01/0.80  % Memory used: 23.048 MB
%------------------------------------------------------------------------------