TSTP Solution File: GEO186+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GEO186+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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 12:08:07 EDT 2023

% Result   : Theorem 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   48 (  11 unt;   0 def)
%            Number of atoms       :  127 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  133 (  54   ~;  50   |;  19   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   62 (;  54   !;   8   ?)

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

fof(f9,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => ~ apart_point_and_line(intersection_point(X,Y),X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => ~ apart_point_and_line(intersection_point(X,Y),Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X,Y,U,V] :
      ( ( distinct_points(X,Y)
        & distinct_lines(U,V) )
     => ( apart_point_and_line(X,U)
        | apart_point_and_line(X,V)
        | apart_point_and_line(Y,U)
        | apart_point_and_line(Y,V) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( distinct_lines(Y,Z)
        | convergent_lines(X,Z) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,conjecture,
    ! [X,Y,U,V] :
      ( ( distinct_points(X,Y)
        & convergent_lines(U,V)
        & ~ apart_point_and_line(X,U)
        & ~ apart_point_and_line(X,V) )
     => ~ distinct_points(X,intersection_point(U,V)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,negated_conjecture,
    ~ ! [X,Y,U,V] :
        ( ( distinct_points(X,Y)
          & convergent_lines(U,V)
          & ~ apart_point_and_line(X,U)
          & ~ apart_point_and_line(X,V) )
       => ~ distinct_points(X,intersection_point(U,V)) ),
    inference(negated_conjecture,[status(cth)],[f15]) ).

fof(f19,plain,
    ! [X0] : ~ convergent_lines(X0,X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f33,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | ~ apart_point_and_line(intersection_point(X,Y),X) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f35,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | ~ apart_point_and_line(intersection_point(X,Y),Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
    inference(cnf_transformation,[status(esa)],[f35]) ).

fof(f37,plain,
    ! [X,Y,U,V] :
      ( ~ distinct_points(X,Y)
      | ~ distinct_lines(U,V)
      | apart_point_and_line(X,U)
      | apart_point_and_line(X,V)
      | apart_point_and_line(Y,U)
      | apart_point_and_line(Y,V) ),
    inference(pre_NNF_transformation,[status(esa)],[f11]) ).

fof(f38,plain,
    ! [X0,X1,X2,X3] :
      ( ~ distinct_points(X0,X1)
      | ~ distinct_lines(X2,X3)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f45,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | distinct_lines(Y,Z)
      | convergent_lines(X,Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f46,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | ! [Z] :
          ( distinct_lines(Y,Z)
          | convergent_lines(X,Z) ) ),
    inference(miniscoping,[status(esa)],[f45]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | distinct_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f48,plain,
    ? [X,Y,U,V] :
      ( distinct_points(X,Y)
      & convergent_lines(U,V)
      & ~ apart_point_and_line(X,U)
      & ~ apart_point_and_line(X,V)
      & distinct_points(X,intersection_point(U,V)) ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f49,plain,
    ? [X,U,V] :
      ( ? [Y] : distinct_points(X,Y)
      & convergent_lines(U,V)
      & ~ apart_point_and_line(X,U)
      & ~ apart_point_and_line(X,V)
      & distinct_points(X,intersection_point(U,V)) ),
    inference(miniscoping,[status(esa)],[f48]) ).

fof(f50,plain,
    ( distinct_points(sk0_0,sk0_3)
    & convergent_lines(sk0_1,sk0_2)
    & ~ apart_point_and_line(sk0_0,sk0_1)
    & ~ apart_point_and_line(sk0_0,sk0_2)
    & distinct_points(sk0_0,intersection_point(sk0_1,sk0_2)) ),
    inference(skolemization,[status(esa)],[f49]) ).

fof(f52,plain,
    convergent_lines(sk0_1,sk0_2),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f53,plain,
    ~ apart_point_and_line(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f54,plain,
    ~ apart_point_and_line(sk0_0,sk0_2),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f55,plain,
    distinct_points(sk0_0,intersection_point(sk0_1,sk0_2)),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | distinct_lines(X1,X0) ),
    inference(resolution,[status(thm)],[f47,f19]) ).

fof(f61,plain,
    ! [X0,X1,X2,X3] :
      ( ~ convergent_lines(X0,X1)
      | ~ distinct_points(X2,X3)
      | apart_point_and_line(X2,X1)
      | apart_point_and_line(X2,X0)
      | apart_point_and_line(X3,X1)
      | apart_point_and_line(X3,X0) ),
    inference(resolution,[status(thm)],[f60,f38]) ).

fof(f185,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | apart_point_and_line(sk0_0,X1)
      | apart_point_and_line(sk0_0,X0)
      | apart_point_and_line(intersection_point(sk0_1,sk0_2),X1)
      | apart_point_and_line(intersection_point(sk0_1,sk0_2),X0) ),
    inference(resolution,[status(thm)],[f61,f55]) ).

fof(f191,plain,
    ( spl0_0
  <=> apart_point_and_line(sk0_0,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f192,plain,
    ( apart_point_and_line(sk0_0,sk0_2)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f191]) ).

fof(f194,plain,
    ( spl0_1
  <=> apart_point_and_line(sk0_0,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f195,plain,
    ( apart_point_and_line(sk0_0,sk0_1)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f194]) ).

fof(f197,plain,
    ( spl0_2
  <=> apart_point_and_line(intersection_point(sk0_1,sk0_2),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f198,plain,
    ( apart_point_and_line(intersection_point(sk0_1,sk0_2),sk0_2)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f197]) ).

fof(f200,plain,
    ( spl0_3
  <=> apart_point_and_line(intersection_point(sk0_1,sk0_2),sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f201,plain,
    ( apart_point_and_line(intersection_point(sk0_1,sk0_2),sk0_1)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f200]) ).

fof(f203,plain,
    ( apart_point_and_line(sk0_0,sk0_2)
    | apart_point_and_line(sk0_0,sk0_1)
    | apart_point_and_line(intersection_point(sk0_1,sk0_2),sk0_2)
    | apart_point_and_line(intersection_point(sk0_1,sk0_2),sk0_1) ),
    inference(resolution,[status(thm)],[f185,f52]) ).

fof(f204,plain,
    ( spl0_0
    | spl0_1
    | spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f203,f191,f194,f197,f200]) ).

fof(f223,plain,
    ( ~ convergent_lines(sk0_1,sk0_2)
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f201,f34]) ).

fof(f224,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f223,f52]) ).

fof(f225,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f224]) ).

fof(f226,plain,
    ( ~ convergent_lines(sk0_1,sk0_2)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f198,f36]) ).

fof(f227,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f226,f52]) ).

fof(f228,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f227]) ).

fof(f229,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f192,f54]) ).

fof(f230,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f229]) ).

fof(f231,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f195,f53]) ).

fof(f232,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f231]) ).

fof(f233,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f204,f225,f228,f230,f232]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GEO186+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n027.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 May 30 12:17:03 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 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: 0.026572 seconds
% 0.18/0.36  % CPU time: 0.085053 seconds
% 0.18/0.36  % Memory used: 2.125 MB
%------------------------------------------------------------------------------