TSTP Solution File: GEO202+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO202+1 : TPTP v5.0.0. Released v3.3.0.
% 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 08:54:03 EST 2010

% Result   : Theorem 11.55s
% Output   : CNFRefutation 11.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   54 (  13 unt;   0 def)
%            Number of atoms       :  147 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  140 (  47   ~;  66   |;  16   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 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   :   85 (   0 sgn  57   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,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/tmpz8m_JY/sel_GEO202+1.p_1',cu1) ).

fof(3,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( distinct_lines(X2,X3)
        | convergent_lines(X1,X3) ) ),
    file('/tmp/tmpz8m_JY/sel_GEO202+1.p_1',ceq3) ).

fof(6,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    file('/tmp/tmpz8m_JY/sel_GEO202+1.p_1',ci3) ).

fof(8,axiom,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    file('/tmp/tmpz8m_JY/sel_GEO202+1.p_1',ci1) ).

fof(9,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    file('/tmp/tmpz8m_JY/sel_GEO202+1.p_1',ci4) ).

fof(12,axiom,
    ! [X1] : ~ convergent_lines(X1,X1),
    file('/tmp/tmpz8m_JY/sel_GEO202+1.p_1',apart3) ).

fof(15,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/tmpz8m_JY/sel_GEO202+1.p_1',con) ).

fof(16,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)],[15]) ).

fof(17,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).

fof(19,plain,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).

fof(20,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).

fof(23,plain,
    ! [X1] : ~ convergent_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).

fof(24,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)],[16,theory(equality)]) ).

fof(28,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)],[2]) ).

fof(29,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)],[28]) ).

cnf(30,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)],[29]) ).

fof(31,plain,
    ! [X1,X2,X3] :
      ( ~ convergent_lines(X1,X2)
      | distinct_lines(X2,X3)
      | convergent_lines(X1,X3) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(32,plain,
    ! [X4,X5,X6] :
      ( ~ convergent_lines(X4,X5)
      | distinct_lines(X5,X6)
      | convergent_lines(X4,X6) ),
    inference(variable_rename,[status(thm)],[31]) ).

cnf(33,plain,
    ( convergent_lines(X1,X2)
    | distinct_lines(X3,X2)
    | ~ convergent_lines(X1,X3) ),
    inference(split_conjunct,[status(thm)],[32]) ).

fof(40,plain,
    ! [X1,X2] :
      ( ~ convergent_lines(X1,X2)
      | ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(41,plain,
    ! [X3,X4] :
      ( ~ convergent_lines(X3,X4)
      | ~ apart_point_and_line(intersection_point(X3,X4),X3) ),
    inference(variable_rename,[status(thm)],[40]) ).

cnf(42,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X1)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(46,plain,
    ! [X1,X2] :
      ( ~ distinct_points(X1,X2)
      | ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(47,plain,
    ! [X3,X4] :
      ( ~ distinct_points(X3,X4)
      | ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
    inference(variable_rename,[status(thm)],[46]) ).

cnf(48,plain,
    ( ~ apart_point_and_line(X1,line_connecting(X1,X2))
    | ~ distinct_points(X1,X2) ),
    inference(split_conjunct,[status(thm)],[47]) ).

fof(49,plain,
    ! [X1,X2] :
      ( ~ convergent_lines(X1,X2)
      | ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(50,plain,
    ! [X3,X4] :
      ( ~ convergent_lines(X3,X4)
      | ~ apart_point_and_line(intersection_point(X3,X4),X4) ),
    inference(variable_rename,[status(thm)],[49]) ).

cnf(51,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[50]) ).

fof(56,plain,
    ! [X2] : ~ convergent_lines(X2,X2),
    inference(variable_rename,[status(thm)],[23]) ).

cnf(57,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[56]) ).

fof(64,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)],[24]) ).

fof(65,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)],[64]) ).

fof(66,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)],[65]) ).

cnf(67,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)],[66]) ).

cnf(68,negated_conjecture,
    convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[66]) ).

cnf(69,negated_conjecture,
    distinct_points(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[66]) ).

cnf(70,negated_conjecture,
    distinct_points(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[66]) ).

cnf(72,negated_conjecture,
    ( distinct_lines(line_connecting(esk1_0,esk3_0),X1)
    | convergent_lines(line_connecting(esk1_0,esk2_0),X1) ),
    inference(spm,[status(thm)],[33,68,theory(equality)]) ).

cnf(114,negated_conjecture,
    ( apart_point_and_line(X1,X2)
    | apart_point_and_line(X1,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(X3,X2)
    | apart_point_and_line(X3,line_connecting(esk1_0,esk3_0))
    | convergent_lines(line_connecting(esk1_0,esk2_0),X2)
    | ~ distinct_points(X3,X1) ),
    inference(spm,[status(thm)],[30,72,theory(equality)]) ).

cnf(436,negated_conjecture,
    ( 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(esk1_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)),X1)
    | apart_point_and_line(esk1_0,X1)
    | convergent_lines(line_connecting(esk1_0,esk2_0),X1) ),
    inference(spm,[status(thm)],[114,67,theory(equality)]) ).

cnf(2941,negated_conjecture,
    ( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),X1)
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk1_0,X1)
    | convergent_lines(line_connecting(esk1_0,esk2_0),X1)
    | ~ convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[51,436,theory(equality)]) ).

cnf(2948,negated_conjecture,
    ( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),X1)
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk1_0,X1)
    | convergent_lines(line_connecting(esk1_0,esk2_0),X1)
    | $false ),
    inference(rw,[status(thm)],[2941,68,theory(equality)]) ).

cnf(2949,negated_conjecture,
    ( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),X1)
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk1_0,X1)
    | convergent_lines(line_connecting(esk1_0,esk2_0),X1) ),
    inference(cn,[status(thm)],[2948,theory(equality)]) ).

cnf(153262,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,esk2_0))
    | ~ convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[42,2949,theory(equality)]) ).

cnf(153266,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,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[153262,68,theory(equality)]) ).

cnf(153267,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,esk2_0)) ),
    inference(cn,[status(thm)],[153266,theory(equality)]) ).

cnf(153268,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(sr,[status(thm)],[153267,57,theory(equality)]) ).

cnf(153269,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | ~ distinct_points(esk1_0,esk3_0) ),
    inference(spm,[status(thm)],[48,153268,theory(equality)]) ).

cnf(153272,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[153269,69,theory(equality)]) ).

cnf(153273,negated_conjecture,
    apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)),
    inference(cn,[status(thm)],[153272,theory(equality)]) ).

cnf(153274,negated_conjecture,
    ~ distinct_points(esk1_0,esk2_0),
    inference(spm,[status(thm)],[48,153273,theory(equality)]) ).

cnf(153278,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[153274,70,theory(equality)]) ).

cnf(153279,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[153278,theory(equality)]) ).

cnf(153280,negated_conjecture,
    $false,
    153279,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO202+1.p
% --creating new selector for [GEO006+0.ax]
% -running prover on /tmp/tmpz8m_JY/sel_GEO202+1.p_1 with time limit 29
% -prover status Theorem
% Problem GEO202+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO202+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO202+1.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
% 
%------------------------------------------------------------------------------