TSTP Solution File: GEO202+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO202+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 08:54:22 EST 2010

% Result   : Theorem 13.47s
% Output   : CNFRefutation 13.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   59 (  14 unt;   0 def)
%            Number of atoms       :  158 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  152 (  53   ~;  71   |;  16   &)
%                                         (   2 <=>;  10  =>;   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   :   92 (   0 sgn  62   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,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/tmp3K6RTY/sel_GEO202+3.p_1',cu1) ).

fof(6,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( distinct_lines(X2,X3)
        | convergent_lines(X1,X3) ) ),
    file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',ceq3) ).

fof(9,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',ci3) ).

fof(11,axiom,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',ci1) ).

fof(12,axiom,
    ! [X1,X2] :
      ( equal_points(X1,X2)
    <=> ~ distinct_points(X1,X2) ),
    file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',ax1) ).

fof(14,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',ci4) ).

fof(17,axiom,
    ! [X1] : ~ convergent_lines(X1,X1),
    file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',apart3) ).

fof(20,conjecture,
    ! [X1,X2,X3] :
      ( ( distinct_points(X1,X2)
        & distinct_points(X1,X3)
        & convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
     => equal_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
    file('/tmp/tmp3K6RTY/sel_GEO202+3.p_1',con) ).

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

fof(23,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).

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

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

fof(27,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).

fof(29,plain,
    ! [X1] : ~ convergent_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[17,theory(equality)]) ).

fof(38,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)],[4]) ).

fof(39,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)],[38]) ).

cnf(40,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)],[39]) ).

fof(44,plain,
    ! [X1,X2,X3] :
      ( ~ convergent_lines(X1,X2)
      | distinct_lines(X2,X3)
      | convergent_lines(X1,X3) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(45,plain,
    ! [X4,X5,X6] :
      ( ~ convergent_lines(X4,X5)
      | distinct_lines(X5,X6)
      | convergent_lines(X4,X6) ),
    inference(variable_rename,[status(thm)],[44]) ).

cnf(46,plain,
    ( convergent_lines(X1,X2)
    | distinct_lines(X3,X2)
    | ~ convergent_lines(X1,X3) ),
    inference(split_conjunct,[status(thm)],[45]) ).

fof(53,plain,
    ! [X1,X2] :
      ( ~ convergent_lines(X1,X2)
      | ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(54,plain,
    ! [X3,X4] :
      ( ~ convergent_lines(X3,X4)
      | ~ apart_point_and_line(intersection_point(X3,X4),X3) ),
    inference(variable_rename,[status(thm)],[53]) ).

cnf(55,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X1)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[54]) ).

fof(59,plain,
    ! [X1,X2] :
      ( ~ distinct_points(X1,X2)
      | ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[25]) ).

fof(60,plain,
    ! [X3,X4] :
      ( ~ distinct_points(X3,X4)
      | ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
    inference(variable_rename,[status(thm)],[59]) ).

cnf(61,plain,
    ( ~ apart_point_and_line(X1,line_connecting(X1,X2))
    | ~ distinct_points(X1,X2) ),
    inference(split_conjunct,[status(thm)],[60]) ).

fof(62,plain,
    ! [X1,X2] :
      ( ( ~ equal_points(X1,X2)
        | ~ distinct_points(X1,X2) )
      & ( distinct_points(X1,X2)
        | equal_points(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[26]) ).

fof(63,plain,
    ! [X3,X4] :
      ( ( ~ equal_points(X3,X4)
        | ~ distinct_points(X3,X4) )
      & ( distinct_points(X3,X4)
        | equal_points(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[62]) ).

cnf(64,plain,
    ( equal_points(X1,X2)
    | distinct_points(X1,X2) ),
    inference(split_conjunct,[status(thm)],[63]) ).

fof(69,plain,
    ! [X1,X2] :
      ( ~ convergent_lines(X1,X2)
      | ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(70,plain,
    ! [X3,X4] :
      ( ~ convergent_lines(X3,X4)
      | ~ apart_point_and_line(intersection_point(X3,X4),X4) ),
    inference(variable_rename,[status(thm)],[69]) ).

cnf(71,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[70]) ).

fof(77,plain,
    ! [X2] : ~ convergent_lines(X2,X2),
    inference(variable_rename,[status(thm)],[29]) ).

cnf(78,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[77]) ).

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

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

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

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

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

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

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

cnf(96,negated_conjecture,
    distinct_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0),
    inference(spm,[status(thm)],[88,64,theory(equality)]) ).

cnf(97,negated_conjecture,
    ( convergent_lines(line_connecting(esk1_0,esk2_0),X1)
    | distinct_lines(line_connecting(esk1_0,esk3_0),X1) ),
    inference(spm,[status(thm)],[46,89,theory(equality)]) ).

cnf(139,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)],[40,97,theory(equality)]) ).

cnf(474,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)],[139,96,theory(equality)]) ).

cnf(3103,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)],[71,474,theory(equality)]) ).

cnf(3106,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)],[3103,89,theory(equality)]) ).

cnf(3107,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)],[3106,theory(equality)]) ).

cnf(175210,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)],[55,3107,theory(equality)]) ).

cnf(175214,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)],[175210,89,theory(equality)]) ).

cnf(175215,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)],[175214,theory(equality)]) ).

cnf(175216,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)],[175215,78,theory(equality)]) ).

cnf(175218,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | ~ distinct_points(esk1_0,esk3_0) ),
    inference(spm,[status(thm)],[61,175216,theory(equality)]) ).

cnf(175220,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[175218,90,theory(equality)]) ).

cnf(175221,negated_conjecture,
    apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)),
    inference(cn,[status(thm)],[175220,theory(equality)]) ).

cnf(175223,negated_conjecture,
    ~ distinct_points(esk1_0,esk2_0),
    inference(spm,[status(thm)],[61,175221,theory(equality)]) ).

cnf(175226,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[175223,91,theory(equality)]) ).

cnf(175227,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[175226,theory(equality)]) ).

cnf(175228,negated_conjecture,
    $false,
    175227,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO202+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/tmp3K6RTY/sel_GEO202+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO202+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO202+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO202+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
% 
%------------------------------------------------------------------------------