TSTP Solution File: GEO194+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO194+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art02.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 08:50:36 EST 2010

% Result   : Theorem 0.40s
% Output   : CNFRefutation 0.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   62 (  11 unt;   0 def)
%            Number of atoms       :  188 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  171 (  45   ~;  97   |;  17   &)
%                                         (   0 <=>;  12  =>;   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    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  118 (   9 sgn  64   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( convergent_lines(X1,X3)
        | convergent_lines(X2,X3) ) ),
    file('/tmp/tmpo7Nhti/sel_GEO194+1.p_1',ax6) ).

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/tmpo7Nhti/sel_GEO194+1.p_1',cu1) ).

fof(3,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( distinct_lines(X2,X3)
        | convergent_lines(X1,X3) ) ),
    file('/tmp/tmpo7Nhti/sel_GEO194+1.p_1',ceq3) ).

fof(5,axiom,
    ! [X1,X2,X3] :
      ( apart_point_and_line(X1,X2)
     => ( distinct_points(X1,X3)
        | apart_point_and_line(X3,X2) ) ),
    file('/tmp/tmpo7Nhti/sel_GEO194+1.p_1',ceq1) ).

fof(6,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    file('/tmp/tmpo7Nhti/sel_GEO194+1.p_1',ci3) ).

fof(7,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    file('/tmp/tmpo7Nhti/sel_GEO194+1.p_1',ci4) ).

fof(10,axiom,
    ! [X1] : ~ convergent_lines(X1,X1),
    file('/tmp/tmpo7Nhti/sel_GEO194+1.p_1',apart3) ).

fof(13,conjecture,
    ! [X1,X2,X3] :
      ( ( convergent_lines(X1,X2)
        & convergent_lines(X3,X2)
        & convergent_lines(X1,X3) )
     => ( apart_point_and_line(intersection_point(X1,X2),X3)
       => apart_point_and_line(intersection_point(X1,X3),X2) ) ),
    file('/tmp/tmpo7Nhti/sel_GEO194+1.p_1',con) ).

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

fof(15,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(16,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).

fof(19,plain,
    ! [X1] : ~ convergent_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).

fof(20,plain,
    ! [X1,X2,X3] :
      ( ~ convergent_lines(X1,X2)
      | convergent_lines(X1,X3)
      | convergent_lines(X2,X3) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(21,plain,
    ! [X4,X5,X6] :
      ( ~ convergent_lines(X4,X5)
      | convergent_lines(X4,X6)
      | convergent_lines(X5,X6) ),
    inference(variable_rename,[status(thm)],[20]) ).

cnf(22,plain,
    ( convergent_lines(X1,X2)
    | convergent_lines(X3,X2)
    | ~ convergent_lines(X3,X1) ),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(23,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(24,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)],[23]) ).

cnf(25,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)],[24]) ).

fof(26,plain,
    ! [X1,X2,X3] :
      ( ~ convergent_lines(X1,X2)
      | distinct_lines(X2,X3)
      | convergent_lines(X1,X3) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(27,plain,
    ! [X4,X5,X6] :
      ( ~ convergent_lines(X4,X5)
      | distinct_lines(X5,X6)
      | convergent_lines(X4,X6) ),
    inference(variable_rename,[status(thm)],[26]) ).

cnf(28,plain,
    ( convergent_lines(X1,X2)
    | distinct_lines(X3,X2)
    | ~ convergent_lines(X1,X3) ),
    inference(split_conjunct,[status(thm)],[27]) ).

fof(32,plain,
    ! [X1,X2,X3] :
      ( ~ apart_point_and_line(X1,X2)
      | distinct_points(X1,X3)
      | apart_point_and_line(X3,X2) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(33,plain,
    ! [X4,X5,X6] :
      ( ~ apart_point_and_line(X4,X5)
      | distinct_points(X4,X6)
      | apart_point_and_line(X6,X5) ),
    inference(variable_rename,[status(thm)],[32]) ).

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

fof(35,plain,
    ! [X1,X2] :
      ( ~ convergent_lines(X1,X2)
      | ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(36,plain,
    ! [X3,X4] :
      ( ~ convergent_lines(X3,X4)
      | ~ apart_point_and_line(intersection_point(X3,X4),X3) ),
    inference(variable_rename,[status(thm)],[35]) ).

cnf(37,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X1)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[36]) ).

fof(38,plain,
    ! [X1,X2] :
      ( ~ convergent_lines(X1,X2)
      | ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(39,plain,
    ! [X3,X4] :
      ( ~ convergent_lines(X3,X4)
      | ~ apart_point_and_line(intersection_point(X3,X4),X4) ),
    inference(variable_rename,[status(thm)],[38]) ).

cnf(40,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[39]) ).

fof(45,plain,
    ! [X2] : ~ convergent_lines(X2,X2),
    inference(variable_rename,[status(thm)],[19]) ).

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

fof(53,negated_conjecture,
    ? [X1,X2,X3] :
      ( convergent_lines(X1,X2)
      & convergent_lines(X3,X2)
      & convergent_lines(X1,X3)
      & apart_point_and_line(intersection_point(X1,X2),X3)
      & ~ apart_point_and_line(intersection_point(X1,X3),X2) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(54,negated_conjecture,
    ? [X4,X5,X6] :
      ( convergent_lines(X4,X5)
      & convergent_lines(X6,X5)
      & convergent_lines(X4,X6)
      & apart_point_and_line(intersection_point(X4,X5),X6)
      & ~ apart_point_and_line(intersection_point(X4,X6),X5) ),
    inference(variable_rename,[status(thm)],[53]) ).

fof(55,negated_conjecture,
    ( convergent_lines(esk1_0,esk2_0)
    & convergent_lines(esk3_0,esk2_0)
    & convergent_lines(esk1_0,esk3_0)
    & apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
    & ~ apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_0) ),
    inference(skolemize,[status(esa)],[54]) ).

cnf(56,negated_conjecture,
    ~ apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_0),
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(57,negated_conjecture,
    apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0),
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(58,negated_conjecture,
    convergent_lines(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(60,negated_conjecture,
    convergent_lines(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(61,negated_conjecture,
    ( convergent_lines(esk2_0,X1)
    | convergent_lines(esk1_0,X1) ),
    inference(spm,[status(thm)],[22,60,theory(equality)]) ).

cnf(67,negated_conjecture,
    ( apart_point_and_line(X1,esk3_0)
    | distinct_points(intersection_point(esk1_0,esk2_0),X1) ),
    inference(spm,[status(thm)],[34,57,theory(equality)]) ).

cnf(70,negated_conjecture,
    ( convergent_lines(X1,X2)
    | convergent_lines(esk1_0,X2)
    | convergent_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[22,61,theory(equality)]) ).

cnf(119,negated_conjecture,
    ( convergent_lines(esk2_0,X1)
    | convergent_lines(X1,esk1_0) ),
    inference(spm,[status(thm)],[46,70,theory(equality)]) ).

cnf(131,negated_conjecture,
    ( convergent_lines(X1,X2)
    | convergent_lines(esk2_0,X2)
    | convergent_lines(X1,esk1_0) ),
    inference(spm,[status(thm)],[22,119,theory(equality)]) ).

cnf(145,negated_conjecture,
    ( convergent_lines(X1,esk1_0)
    | convergent_lines(X1,esk2_0) ),
    inference(spm,[status(thm)],[46,131,theory(equality)]) ).

cnf(161,negated_conjecture,
    ( distinct_lines(esk1_0,X1)
    | convergent_lines(X2,X1)
    | convergent_lines(X2,esk2_0) ),
    inference(spm,[status(thm)],[28,145,theory(equality)]) ).

cnf(452,negated_conjecture,
    ( distinct_lines(esk1_0,esk2_0)
    | convergent_lines(X3,esk2_0) ),
    inference(ef,[status(thm)],[161,theory(equality)]) ).

cnf(465,negated_conjecture,
    ( apart_point_and_line(X1,esk2_0)
    | apart_point_and_line(X1,esk1_0)
    | apart_point_and_line(X2,esk2_0)
    | apart_point_and_line(X2,esk1_0)
    | convergent_lines(X3,esk2_0)
    | ~ distinct_points(X2,X1) ),
    inference(spm,[status(thm)],[25,452,theory(equality)]) ).

cnf(3149,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
    | apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
    | apart_point_and_line(X1,esk1_0)
    | apart_point_and_line(X1,esk2_0)
    | convergent_lines(X2,esk2_0)
    | apart_point_and_line(X1,esk3_0) ),
    inference(spm,[status(thm)],[465,67,theory(equality)]) ).

cnf(3387,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
    | apart_point_and_line(X1,esk3_0)
    | apart_point_and_line(X1,esk2_0)
    | apart_point_and_line(X1,esk1_0)
    | convergent_lines(X2,esk2_0)
    | ~ convergent_lines(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[37,3149,theory(equality)]) ).

cnf(3393,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
    | apart_point_and_line(X1,esk3_0)
    | apart_point_and_line(X1,esk2_0)
    | apart_point_and_line(X1,esk1_0)
    | convergent_lines(X2,esk2_0)
    | $false ),
    inference(rw,[status(thm)],[3387,60,theory(equality)]) ).

cnf(3394,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
    | apart_point_and_line(X1,esk3_0)
    | apart_point_and_line(X1,esk2_0)
    | apart_point_and_line(X1,esk1_0)
    | convergent_lines(X2,esk2_0) ),
    inference(cn,[status(thm)],[3393,theory(equality)]) ).

cnf(3397,negated_conjecture,
    ( apart_point_and_line(X1,esk1_0)
    | apart_point_and_line(X1,esk2_0)
    | apart_point_and_line(X1,esk3_0)
    | convergent_lines(X2,esk2_0)
    | ~ convergent_lines(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[40,3394,theory(equality)]) ).

cnf(3404,negated_conjecture,
    ( apart_point_and_line(X1,esk1_0)
    | apart_point_and_line(X1,esk2_0)
    | apart_point_and_line(X1,esk3_0)
    | convergent_lines(X2,esk2_0)
    | $false ),
    inference(rw,[status(thm)],[3397,60,theory(equality)]) ).

cnf(3405,negated_conjecture,
    ( apart_point_and_line(X1,esk1_0)
    | apart_point_and_line(X1,esk2_0)
    | apart_point_and_line(X1,esk3_0)
    | convergent_lines(X2,esk2_0) ),
    inference(cn,[status(thm)],[3404,theory(equality)]) ).

cnf(3433,negated_conjecture,
    ( apart_point_and_line(X1,esk3_0)
    | apart_point_and_line(X1,esk2_0)
    | apart_point_and_line(X1,esk1_0) ),
    inference(spm,[status(thm)],[46,3405,theory(equality)]) ).

cnf(3440,negated_conjecture,
    ( apart_point_and_line(intersection_point(X1,esk3_0),esk1_0)
    | apart_point_and_line(intersection_point(X1,esk3_0),esk2_0)
    | ~ convergent_lines(X1,esk3_0) ),
    inference(spm,[status(thm)],[40,3433,theory(equality)]) ).

cnf(3444,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_0)
    | ~ convergent_lines(esk1_0,esk3_0) ),
    inference(spm,[status(thm)],[37,3440,theory(equality)]) ).

cnf(3447,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_0)
    | $false ),
    inference(rw,[status(thm)],[3444,58,theory(equality)]) ).

cnf(3448,negated_conjecture,
    apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_0),
    inference(cn,[status(thm)],[3447,theory(equality)]) ).

cnf(3449,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[3448,56,theory(equality)]) ).

cnf(3450,negated_conjecture,
    $false,
    3449,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO194+1.p
% --creating new selector for [GEO006+0.ax]
% -running prover on /tmp/tmpo7Nhti/sel_GEO194+1.p_1 with time limit 29
% -prover status Theorem
% Problem GEO194+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO194+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO194+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
% 
%------------------------------------------------------------------------------