TSTP Solution File: GEO203+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO203+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 08:54:42 EST 2010

% Result   : Theorem 0.43s
% Output   : CNFRefutation 0.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   49 (  10 unt;   0 def)
%            Number of atoms       :  130 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  127 (  46   ~;  54   |;  16   &)
%                                         (   2 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   70 (   0 sgn  50   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( equal_lines(X1,X2)
    <=> ~ distinct_lines(X1,X2) ),
    file('/tmp/tmpkmOnKC/sel_GEO203+3.p_1',ax2) ).

fof(5,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/tmpkmOnKC/sel_GEO203+3.p_1',cu1) ).

fof(10,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    file('/tmp/tmpkmOnKC/sel_GEO203+3.p_1',ci3) ).

fof(11,axiom,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
    file('/tmp/tmpkmOnKC/sel_GEO203+3.p_1',ci2) ).

fof(12,axiom,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    file('/tmp/tmpkmOnKC/sel_GEO203+3.p_1',ci1) ).

fof(20,conjecture,
    ! [X1,X2,X3] :
      ( ( convergent_lines(X1,X2)
        & convergent_lines(X1,X3)
        & distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) )
     => equal_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
    file('/tmp/tmpkmOnKC/sel_GEO203+3.p_1',con) ).

fof(21,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( convergent_lines(X1,X2)
          & convergent_lines(X1,X3)
          & distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) )
       => equal_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
    inference(assume_negation,[status(cth)],[20]) ).

fof(22,plain,
    ! [X1,X2] :
      ( equal_lines(X1,X2)
    <=> ~ distinct_lines(X1,X2) ),
    inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).

fof(24,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).

fof(25,plain,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).

fof(26,plain,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).

fof(30,plain,
    ! [X1,X2] :
      ( ( ~ equal_lines(X1,X2)
        | ~ distinct_lines(X1,X2) )
      & ( distinct_lines(X1,X2)
        | equal_lines(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(31,plain,
    ! [X3,X4] :
      ( ( ~ equal_lines(X3,X4)
        | ~ distinct_lines(X3,X4) )
      & ( distinct_lines(X3,X4)
        | equal_lines(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[30]) ).

cnf(32,plain,
    ( equal_lines(X1,X2)
    | distinct_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[31]) ).

fof(42,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)],[5]) ).

fof(43,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)],[42]) ).

cnf(44,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)],[43]) ).

fof(57,plain,
    ! [X1,X2] :
      ( ~ convergent_lines(X1,X2)
      | ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(58,plain,
    ! [X3,X4] :
      ( ~ convergent_lines(X3,X4)
      | ~ apart_point_and_line(intersection_point(X3,X4),X3) ),
    inference(variable_rename,[status(thm)],[57]) ).

cnf(59,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X1)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[58]) ).

fof(60,plain,
    ! [X1,X2] :
      ( ~ distinct_points(X1,X2)
      | ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[25]) ).

fof(61,plain,
    ! [X3,X4] :
      ( ~ distinct_points(X3,X4)
      | ~ apart_point_and_line(X4,line_connecting(X3,X4)) ),
    inference(variable_rename,[status(thm)],[60]) ).

cnf(62,plain,
    ( ~ apart_point_and_line(X1,line_connecting(X2,X1))
    | ~ distinct_points(X2,X1) ),
    inference(split_conjunct,[status(thm)],[61]) ).

fof(63,plain,
    ! [X1,X2] :
      ( ~ distinct_points(X1,X2)
      | ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[26]) ).

fof(64,plain,
    ! [X3,X4] :
      ( ~ distinct_points(X3,X4)
      | ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
    inference(variable_rename,[status(thm)],[63]) ).

cnf(65,plain,
    ( ~ apart_point_and_line(X1,line_connecting(X1,X2))
    | ~ distinct_points(X1,X2) ),
    inference(split_conjunct,[status(thm)],[64]) ).

fof(85,negated_conjecture,
    ? [X1,X2,X3] :
      ( convergent_lines(X1,X2)
      & convergent_lines(X1,X3)
      & distinct_points(intersection_point(X1,X2),intersection_point(X1,X3))
      & ~ equal_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(86,negated_conjecture,
    ? [X4,X5,X6] :
      ( convergent_lines(X4,X5)
      & convergent_lines(X4,X6)
      & distinct_points(intersection_point(X4,X5),intersection_point(X4,X6))
      & ~ equal_lines(line_connecting(intersection_point(X4,X5),intersection_point(X4,X6)),X4) ),
    inference(variable_rename,[status(thm)],[85]) ).

fof(87,negated_conjecture,
    ( convergent_lines(esk1_0,esk2_0)
    & convergent_lines(esk1_0,esk3_0)
    & distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0))
    & ~ equal_lines(line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),esk1_0) ),
    inference(skolemize,[status(esa)],[86]) ).

cnf(88,negated_conjecture,
    ~ equal_lines(line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),esk1_0),
    inference(split_conjunct,[status(thm)],[87]) ).

cnf(89,negated_conjecture,
    distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[87]) ).

cnf(90,negated_conjecture,
    convergent_lines(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[87]) ).

cnf(91,negated_conjecture,
    convergent_lines(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[87]) ).

cnf(96,negated_conjecture,
    distinct_lines(line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),esk1_0),
    inference(spm,[status(thm)],[88,32,theory(equality)]) ).

cnf(101,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk3_0),X1)
    | apart_point_and_line(intersection_point(esk1_0,esk3_0),X2)
    | apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
    | apart_point_and_line(intersection_point(esk1_0,esk2_0),X2)
    | ~ distinct_lines(X2,X1) ),
    inference(spm,[status(thm)],[44,89,theory(equality)]) ).

cnf(131,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
    | apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
    | apart_point_and_line(intersection_point(esk1_0,esk3_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
    | apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0) ),
    inference(spm,[status(thm)],[101,96,theory(equality)]) ).

cnf(494,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
    | apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
    | apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
    | ~ distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[62,131,theory(equality)]) ).

cnf(497,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
    | apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
    | apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
    | $false ),
    inference(rw,[status(thm)],[494,89,theory(equality)]) ).

cnf(498,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
    | apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
    | apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0) ),
    inference(cn,[status(thm)],[497,theory(equality)]) ).

cnf(5628,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
    | apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
    | ~ distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[65,498,theory(equality)]) ).

cnf(5630,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
    | apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
    | $false ),
    inference(rw,[status(thm)],[5628,89,theory(equality)]) ).

cnf(5631,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
    | apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0) ),
    inference(cn,[status(thm)],[5630,theory(equality)]) ).

cnf(5634,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
    | ~ convergent_lines(esk1_0,esk3_0) ),
    inference(spm,[status(thm)],[59,5631,theory(equality)]) ).

cnf(5635,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
    | $false ),
    inference(rw,[status(thm)],[5634,90,theory(equality)]) ).

cnf(5636,negated_conjecture,
    apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0),
    inference(cn,[status(thm)],[5635,theory(equality)]) ).

cnf(5639,negated_conjecture,
    ~ convergent_lines(esk1_0,esk2_0),
    inference(spm,[status(thm)],[59,5636,theory(equality)]) ).

cnf(5641,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[5639,91,theory(equality)]) ).

cnf(5642,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[5641,theory(equality)]) ).

cnf(5643,negated_conjecture,
    $false,
    5642,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO203+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/tmpkmOnKC/sel_GEO203+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO203+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO203+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO203+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
% 
%------------------------------------------------------------------------------