TSTP Solution File: GEO173+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO173+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 08:43:58 EST 2010

% Result   : Theorem 0.18s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   34 (   9 unt;   0 def)
%            Number of atoms       :   96 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   96 (  34   ~;  38   |;  17   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   54 (   0 sgn  36   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X3,X4,X6,X7] :
      ( ( distinct_points(X3,X4)
        & distinct_lines(X6,X7) )
     => ( apart_point_and_line(X3,X6)
        | apart_point_and_line(X3,X7)
        | apart_point_and_line(X4,X6)
        | apart_point_and_line(X4,X7) ) ),
    file('/tmp/tmpXXkVpw/sel_GEO173+3.p_1',cu1) ).

fof(8,axiom,
    ! [X3,X4] :
      ( distinct_points(X3,X4)
     => ~ apart_point_and_line(X4,line_connecting(X3,X4)) ),
    file('/tmp/tmpXXkVpw/sel_GEO173+3.p_1',ci2) ).

fof(9,axiom,
    ! [X3,X4] :
      ( distinct_points(X3,X4)
     => ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
    file('/tmp/tmpXXkVpw/sel_GEO173+3.p_1',ci1) ).

fof(16,conjecture,
    ! [X3,X4,X6,X7] :
      ( ( distinct_points(X3,X4)
        & convergent_lines(X6,X7)
        & distinct_lines(X6,line_connecting(X3,X4)) )
     => ( apart_point_and_line(X3,X6)
        | apart_point_and_line(X4,X6) ) ),
    file('/tmp/tmpXXkVpw/sel_GEO173+3.p_1',con) ).

fof(17,negated_conjecture,
    ~ ! [X3,X4,X6,X7] :
        ( ( distinct_points(X3,X4)
          & convergent_lines(X6,X7)
          & distinct_lines(X6,line_connecting(X3,X4)) )
       => ( apart_point_and_line(X3,X6)
          | apart_point_and_line(X4,X6) ) ),
    inference(assume_negation,[status(cth)],[16]) ).

fof(18,plain,
    ! [X3,X4] :
      ( distinct_points(X3,X4)
     => ~ apart_point_and_line(X4,line_connecting(X3,X4)) ),
    inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).

fof(19,plain,
    ! [X3,X4] :
      ( distinct_points(X3,X4)
     => ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
    inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).

fof(32,plain,
    ! [X3,X4,X6,X7] :
      ( ~ distinct_points(X3,X4)
      | ~ distinct_lines(X6,X7)
      | apart_point_and_line(X3,X6)
      | apart_point_and_line(X3,X7)
      | apart_point_and_line(X4,X6)
      | apart_point_and_line(X4,X7) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(33,plain,
    ! [X8,X9,X10,X11] :
      ( ~ distinct_points(X8,X9)
      | ~ distinct_lines(X10,X11)
      | apart_point_and_line(X8,X10)
      | apart_point_and_line(X8,X11)
      | apart_point_and_line(X9,X10)
      | apart_point_and_line(X9,X11) ),
    inference(variable_rename,[status(thm)],[32]) ).

cnf(34,plain,
    ( apart_point_and_line(X1,X2)
    | apart_point_and_line(X1,X3)
    | apart_point_and_line(X4,X2)
    | apart_point_and_line(X4,X3)
    | ~ distinct_lines(X3,X2)
    | ~ distinct_points(X4,X1) ),
    inference(split_conjunct,[status(thm)],[33]) ).

fof(44,plain,
    ! [X3,X4] :
      ( ~ distinct_points(X3,X4)
      | ~ apart_point_and_line(X4,line_connecting(X3,X4)) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(45,plain,
    ! [X5,X6] :
      ( ~ distinct_points(X5,X6)
      | ~ apart_point_and_line(X6,line_connecting(X5,X6)) ),
    inference(variable_rename,[status(thm)],[44]) ).

cnf(46,plain,
    ( ~ apart_point_and_line(X1,line_connecting(X2,X1))
    | ~ distinct_points(X2,X1) ),
    inference(split_conjunct,[status(thm)],[45]) ).

fof(47,plain,
    ! [X3,X4] :
      ( ~ distinct_points(X3,X4)
      | ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(48,plain,
    ! [X5,X6] :
      ( ~ distinct_points(X5,X6)
      | ~ apart_point_and_line(X5,line_connecting(X5,X6)) ),
    inference(variable_rename,[status(thm)],[47]) ).

cnf(49,plain,
    ( ~ apart_point_and_line(X1,line_connecting(X1,X2))
    | ~ distinct_points(X1,X2) ),
    inference(split_conjunct,[status(thm)],[48]) ).

fof(65,negated_conjecture,
    ? [X3,X4,X6,X7] :
      ( distinct_points(X3,X4)
      & convergent_lines(X6,X7)
      & distinct_lines(X6,line_connecting(X3,X4))
      & ~ apart_point_and_line(X3,X6)
      & ~ apart_point_and_line(X4,X6) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(66,negated_conjecture,
    ? [X8,X9,X10,X11] :
      ( distinct_points(X8,X9)
      & convergent_lines(X10,X11)
      & distinct_lines(X10,line_connecting(X8,X9))
      & ~ apart_point_and_line(X8,X10)
      & ~ apart_point_and_line(X9,X10) ),
    inference(variable_rename,[status(thm)],[65]) ).

fof(67,negated_conjecture,
    ( distinct_points(esk1_0,esk2_0)
    & convergent_lines(esk3_0,esk4_0)
    & distinct_lines(esk3_0,line_connecting(esk1_0,esk2_0))
    & ~ apart_point_and_line(esk1_0,esk3_0)
    & ~ apart_point_and_line(esk2_0,esk3_0) ),
    inference(skolemize,[status(esa)],[66]) ).

cnf(68,negated_conjecture,
    ~ apart_point_and_line(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(69,negated_conjecture,
    ~ apart_point_and_line(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(70,negated_conjecture,
    distinct_lines(esk3_0,line_connecting(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(72,negated_conjecture,
    distinct_points(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(82,negated_conjecture,
    ( apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(X1,esk3_0)
    | apart_point_and_line(X2,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(X2,esk3_0)
    | ~ distinct_points(X2,X1) ),
    inference(spm,[status(thm)],[34,70,theory(equality)]) ).

cnf(142,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,esk3_0)
    | apart_point_and_line(esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[82,72,theory(equality)]) ).

cnf(150,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk2_0,esk3_0) ),
    inference(sr,[status(thm)],[142,69,theory(equality)]) ).

cnf(151,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)) ),
    inference(sr,[status(thm)],[150,68,theory(equality)]) ).

cnf(203,negated_conjecture,
    ( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
    | ~ distinct_points(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[49,151,theory(equality)]) ).

cnf(206,negated_conjecture,
    ( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[203,72,theory(equality)]) ).

cnf(207,negated_conjecture,
    apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)),
    inference(cn,[status(thm)],[206,theory(equality)]) ).

cnf(208,negated_conjecture,
    ~ distinct_points(esk1_0,esk2_0),
    inference(spm,[status(thm)],[46,207,theory(equality)]) ).

cnf(212,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[208,72,theory(equality)]) ).

cnf(213,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[212,theory(equality)]) ).

cnf(214,negated_conjecture,
    $false,
    213,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO173+3.p
% --creating new selector for [GEO006+3.ax, GEO006+0.ax, GEO006+1.ax, GEO006+2.ax, GEO006+4.ax, GEO006+5.ax, GEO006+6.ax]
% -running prover on /tmp/tmpXXkVpw/sel_GEO173+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO173+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO173+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO173+3.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------