TSTP Solution File: GEO202+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO202+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 08:54:15 EST 2010

% Result   : Theorem 67.47s
% Output   : CNFRefutation 67.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   53 (  12 unt;   0 def)
%            Number of atoms       :  163 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  163 (  53   ~;  78   |;  23   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   86 (   0 sgn  54   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] :
      ( distinct_points(X1,X2)
     => ( apart_point_and_line(X3,line_connecting(X1,X2))
       => ( distinct_points(X3,X1)
          & distinct_points(X3,X2) ) ) ),
    file('/tmp/tmpOq2txv/sel_GEO202+2.p_2',con1) ).

fof(2,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( ( apart_point_and_line(X3,X1)
          | apart_point_and_line(X3,X2) )
       => distinct_points(X3,intersection_point(X1,X2)) ) ),
    file('/tmp/tmpOq2txv/sel_GEO202+2.p_2',con2) ).

fof(3,axiom,
    ! [X1,X2,X4,X5] :
      ( ( distinct_points(X1,X2)
        & distinct_lines(X4,X5) )
     => ( apart_point_and_line(X1,X4)
        | apart_point_and_line(X1,X5)
        | apart_point_and_line(X2,X4)
        | apart_point_and_line(X2,X5) ) ),
    file('/tmp/tmpOq2txv/sel_GEO202+2.p_2',cu1) ).

fof(4,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => distinct_lines(X1,X2) ),
    file('/tmp/tmpOq2txv/sel_GEO202+2.p_2',ceq3) ).

fof(7,axiom,
    ! [X1] : ~ distinct_points(X1,X1),
    file('/tmp/tmpOq2txv/sel_GEO202+2.p_2',apart1) ).

fof(13,conjecture,
    ! [X1,X2,X3] :
      ( ( distinct_points(X1,X2)
        & distinct_points(X1,X3)
        & convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
     => ~ distinct_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
    file('/tmp/tmpOq2txv/sel_GEO202+2.p_2',con) ).

fof(14,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( distinct_points(X1,X2)
          & distinct_points(X1,X3)
          & convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
       => ~ distinct_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
    inference(assume_negation,[status(cth)],[13]) ).

fof(15,plain,
    ! [X1] : ~ distinct_points(X1,X1),
    inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).

fof(18,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( distinct_points(X1,X2)
          & distinct_points(X1,X3)
          & convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
       => ~ distinct_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
    inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).

fof(19,plain,
    ! [X1,X2,X3] :
      ( ~ distinct_points(X1,X2)
      | ~ apart_point_and_line(X3,line_connecting(X1,X2))
      | ( distinct_points(X3,X1)
        & distinct_points(X3,X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(20,plain,
    ! [X4,X5,X6] :
      ( ~ distinct_points(X4,X5)
      | ~ apart_point_and_line(X6,line_connecting(X4,X5))
      | ( distinct_points(X6,X4)
        & distinct_points(X6,X5) ) ),
    inference(variable_rename,[status(thm)],[19]) ).

fof(21,plain,
    ! [X4,X5,X6] :
      ( ( distinct_points(X6,X4)
        | ~ apart_point_and_line(X6,line_connecting(X4,X5))
        | ~ distinct_points(X4,X5) )
      & ( distinct_points(X6,X5)
        | ~ apart_point_and_line(X6,line_connecting(X4,X5))
        | ~ distinct_points(X4,X5) ) ),
    inference(distribute,[status(thm)],[20]) ).

cnf(23,plain,
    ( distinct_points(X3,X1)
    | ~ distinct_points(X1,X2)
    | ~ apart_point_and_line(X3,line_connecting(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(24,plain,
    ! [X1,X2,X3] :
      ( ~ convergent_lines(X1,X2)
      | ( ~ apart_point_and_line(X3,X1)
        & ~ apart_point_and_line(X3,X2) )
      | distinct_points(X3,intersection_point(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(25,plain,
    ! [X4,X5,X6] :
      ( ~ convergent_lines(X4,X5)
      | ( ~ apart_point_and_line(X6,X4)
        & ~ apart_point_and_line(X6,X5) )
      | distinct_points(X6,intersection_point(X4,X5)) ),
    inference(variable_rename,[status(thm)],[24]) ).

fof(26,plain,
    ! [X4,X5,X6] :
      ( ( ~ apart_point_and_line(X6,X4)
        | distinct_points(X6,intersection_point(X4,X5))
        | ~ convergent_lines(X4,X5) )
      & ( ~ apart_point_and_line(X6,X5)
        | distinct_points(X6,intersection_point(X4,X5))
        | ~ convergent_lines(X4,X5) ) ),
    inference(distribute,[status(thm)],[25]) ).

cnf(27,plain,
    ( distinct_points(X3,intersection_point(X1,X2))
    | ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(X3,X2) ),
    inference(split_conjunct,[status(thm)],[26]) ).

cnf(28,plain,
    ( distinct_points(X3,intersection_point(X1,X2))
    | ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(X3,X1) ),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(29,plain,
    ! [X1,X2,X4,X5] :
      ( ~ distinct_points(X1,X2)
      | ~ distinct_lines(X4,X5)
      | apart_point_and_line(X1,X4)
      | apart_point_and_line(X1,X5)
      | apart_point_and_line(X2,X4)
      | apart_point_and_line(X2,X5) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(30,plain,
    ! [X6,X7,X8,X9] :
      ( ~ distinct_points(X6,X7)
      | ~ distinct_lines(X8,X9)
      | apart_point_and_line(X6,X8)
      | apart_point_and_line(X6,X9)
      | apart_point_and_line(X7,X8)
      | apart_point_and_line(X7,X9) ),
    inference(variable_rename,[status(thm)],[29]) ).

cnf(31,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)],[30]) ).

fof(32,plain,
    ! [X1,X2] :
      ( ~ convergent_lines(X1,X2)
      | distinct_lines(X1,X2) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(33,plain,
    ! [X3,X4] :
      ( ~ convergent_lines(X3,X4)
      | distinct_lines(X3,X4) ),
    inference(variable_rename,[status(thm)],[32]) ).

cnf(34,plain,
    ( distinct_lines(X1,X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[33]) ).

fof(41,plain,
    ! [X2] : ~ distinct_points(X2,X2),
    inference(variable_rename,[status(thm)],[15]) ).

cnf(42,plain,
    ~ distinct_points(X1,X1),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(56,negated_conjecture,
    ? [X1,X2,X3] :
      ( distinct_points(X1,X2)
      & distinct_points(X1,X3)
      & convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3))
      & distinct_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(57,negated_conjecture,
    ? [X4,X5,X6] :
      ( distinct_points(X4,X5)
      & distinct_points(X4,X6)
      & convergent_lines(line_connecting(X4,X5),line_connecting(X4,X6))
      & distinct_points(intersection_point(line_connecting(X4,X5),line_connecting(X4,X6)),X4) ),
    inference(variable_rename,[status(thm)],[56]) ).

fof(58,negated_conjecture,
    ( distinct_points(esk1_0,esk2_0)
    & distinct_points(esk1_0,esk3_0)
    & convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0))
    & distinct_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0) ),
    inference(skolemize,[status(esa)],[57]) ).

cnf(59,negated_conjecture,
    distinct_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(60,negated_conjecture,
    convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(61,negated_conjecture,
    distinct_points(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(62,negated_conjecture,
    distinct_points(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(68,plain,
    ( ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(spm,[status(thm)],[42,27,theory(equality)]) ).

cnf(70,plain,
    ( ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(spm,[status(thm)],[42,28,theory(equality)]) ).

cnf(73,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_points(X4,X1)
    | ~ convergent_lines(X3,X2) ),
    inference(spm,[status(thm)],[31,34,theory(equality)]) ).

cnf(191,negated_conjecture,
    ( apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(X1,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(X2,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(X2,line_connecting(esk1_0,esk3_0))
    | ~ distinct_points(X1,X2) ),
    inference(spm,[status(thm)],[73,60,theory(equality)]) ).

cnf(722,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[191,59,theory(equality)]) ).

cnf(6093,negated_conjecture,
    ( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | ~ convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[68,722,theory(equality)]) ).

cnf(6101,negated_conjecture,
    ( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | $false ),
    inference(rw,[status(thm)],[6093,60,theory(equality)]) ).

cnf(6102,negated_conjecture,
    ( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0)) ),
    inference(cn,[status(thm)],[6101,theory(equality)]) ).

cnf(472054,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | ~ convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[70,6102,theory(equality)]) ).

cnf(472074,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[472054,60,theory(equality)]) ).

cnf(472075,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)) ),
    inference(cn,[status(thm)],[472074,theory(equality)]) ).

cnf(472078,negated_conjecture,
    ( distinct_points(esk1_0,esk1_0)
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | ~ distinct_points(esk1_0,esk3_0) ),
    inference(spm,[status(thm)],[23,472075,theory(equality)]) ).

cnf(472097,negated_conjecture,
    ( distinct_points(esk1_0,esk1_0)
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[472078,61,theory(equality)]) ).

cnf(472098,negated_conjecture,
    ( distinct_points(esk1_0,esk1_0)
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)) ),
    inference(cn,[status(thm)],[472097,theory(equality)]) ).

cnf(472099,negated_conjecture,
    apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)),
    inference(sr,[status(thm)],[472098,42,theory(equality)]) ).

cnf(472102,negated_conjecture,
    ( distinct_points(esk1_0,esk1_0)
    | ~ distinct_points(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[23,472099,theory(equality)]) ).

cnf(472198,negated_conjecture,
    ( distinct_points(esk1_0,esk1_0)
    | $false ),
    inference(rw,[status(thm)],[472102,62,theory(equality)]) ).

cnf(472199,negated_conjecture,
    distinct_points(esk1_0,esk1_0),
    inference(cn,[status(thm)],[472198,theory(equality)]) ).

cnf(472200,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[472199,42,theory(equality)]) ).

cnf(472201,negated_conjecture,
    $false,
    472200,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO202+2.p
% --creating new selector for [GEO008+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpOq2txv/sel_GEO202+2.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpOq2txv/sel_GEO202+2.p_2 with time limit 81
% -prover status Theorem
% Problem GEO202+2.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO202+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO202+2.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
% 
%------------------------------------------------------------------------------