TSTP Solution File: GEO188+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO188+2 : 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 08:48:28 EST 2010

% Result   : Theorem 0.27s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   59 (  13 unt;   0 def)
%            Number of atoms       :  192 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  178 (  45   ~;  99   |;  26   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   97 (   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/tmpUn3CFE/sel_GEO188+2.p_1',con1) ).

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/tmpUn3CFE/sel_GEO188+2.p_1',cu1) ).

fof(3,axiom,
    ! [X1,X2,X3] :
      ( apart_point_and_line(X1,X2)
     => ( distinct_lines(X2,X3)
        | apart_point_and_line(X1,X3) ) ),
    file('/tmp/tmpUn3CFE/sel_GEO188+2.p_1',ceq2) ).

fof(5,axiom,
    ! [X1] : ~ distinct_points(X1,X1),
    file('/tmp/tmpUn3CFE/sel_GEO188+2.p_1',apart1) ).

fof(7,axiom,
    ! [X1,X2,X3] :
      ( distinct_points(X1,X2)
     => ( distinct_points(X1,X3)
        | distinct_points(X2,X3) ) ),
    file('/tmp/tmpUn3CFE/sel_GEO188+2.p_1',apart4) ).

fof(9,conjecture,
    ! [X1,X2,X3] :
      ( ( distinct_points(X1,X2)
        & distinct_points(X1,X3)
        & distinct_points(X2,X3)
        & ~ apart_point_and_line(X3,line_connecting(X1,X2)) )
     => ~ apart_point_and_line(X1,line_connecting(X3,X2)) ),
    file('/tmp/tmpUn3CFE/sel_GEO188+2.p_1',con) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( distinct_points(X1,X2)
          & distinct_points(X1,X3)
          & distinct_points(X2,X3)
          & ~ apart_point_and_line(X3,line_connecting(X1,X2)) )
       => ~ apart_point_and_line(X1,line_connecting(X3,X2)) ),
    inference(assume_negation,[status(cth)],[9]) ).

fof(11,plain,
    ! [X1] : ~ distinct_points(X1,X1),
    inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).

fof(13,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( distinct_points(X1,X2)
          & distinct_points(X1,X3)
          & distinct_points(X2,X3)
          & ~ apart_point_and_line(X3,line_connecting(X1,X2)) )
       => ~ apart_point_and_line(X1,line_connecting(X3,X2)) ),
    inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).

fof(14,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(15,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)],[14]) ).

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

cnf(17,plain,
    ( distinct_points(X3,X2)
    | ~ distinct_points(X1,X2)
    | ~ apart_point_and_line(X3,line_connecting(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[16]) ).

cnf(18,plain,
    ( distinct_points(X3,X1)
    | ~ distinct_points(X1,X2)
    | ~ apart_point_and_line(X3,line_connecting(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(19,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(20,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)],[19]) ).

cnf(21,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)],[20]) ).

fof(22,plain,
    ! [X1,X2,X3] :
      ( ~ apart_point_and_line(X1,X2)
      | distinct_lines(X2,X3)
      | apart_point_and_line(X1,X3) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(23,plain,
    ! [X4,X5,X6] :
      ( ~ apart_point_and_line(X4,X5)
      | distinct_lines(X5,X6)
      | apart_point_and_line(X4,X6) ),
    inference(variable_rename,[status(thm)],[22]) ).

cnf(24,plain,
    ( apart_point_and_line(X1,X2)
    | distinct_lines(X3,X2)
    | ~ apart_point_and_line(X1,X3) ),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(28,plain,
    ! [X2] : ~ distinct_points(X2,X2),
    inference(variable_rename,[status(thm)],[11]) ).

cnf(29,plain,
    ~ distinct_points(X1,X1),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(32,plain,
    ! [X1,X2,X3] :
      ( ~ distinct_points(X1,X2)
      | distinct_points(X1,X3)
      | distinct_points(X2,X3) ),
    inference(fof_nnf,[status(thm)],[7]) ).

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

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

fof(38,negated_conjecture,
    ? [X1,X2,X3] :
      ( distinct_points(X1,X2)
      & distinct_points(X1,X3)
      & distinct_points(X2,X3)
      & ~ apart_point_and_line(X3,line_connecting(X1,X2))
      & apart_point_and_line(X1,line_connecting(X3,X2)) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(39,negated_conjecture,
    ? [X4,X5,X6] :
      ( distinct_points(X4,X5)
      & distinct_points(X4,X6)
      & distinct_points(X5,X6)
      & ~ apart_point_and_line(X6,line_connecting(X4,X5))
      & apart_point_and_line(X4,line_connecting(X6,X5)) ),
    inference(variable_rename,[status(thm)],[38]) ).

fof(40,negated_conjecture,
    ( distinct_points(esk1_0,esk2_0)
    & distinct_points(esk1_0,esk3_0)
    & distinct_points(esk2_0,esk3_0)
    & ~ apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
    & apart_point_and_line(esk1_0,line_connecting(esk3_0,esk2_0)) ),
    inference(skolemize,[status(esa)],[39]) ).

cnf(41,negated_conjecture,
    apart_point_and_line(esk1_0,line_connecting(esk3_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(42,negated_conjecture,
    ~ apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(43,negated_conjecture,
    distinct_points(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(45,negated_conjecture,
    distinct_points(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(48,negated_conjecture,
    ( distinct_points(esk3_0,X1)
    | distinct_points(esk2_0,X1) ),
    inference(spm,[status(thm)],[34,43,theory(equality)]) ).

cnf(50,negated_conjecture,
    ( distinct_lines(line_connecting(esk3_0,esk2_0),X1)
    | apart_point_and_line(esk1_0,X1) ),
    inference(spm,[status(thm)],[24,41,theory(equality)]) ).

cnf(62,negated_conjecture,
    ( distinct_points(X1,X2)
    | distinct_points(esk3_0,X2)
    | distinct_points(esk2_0,X1) ),
    inference(spm,[status(thm)],[34,48,theory(equality)]) ).

cnf(96,negated_conjecture,
    ( apart_point_and_line(X1,X2)
    | apart_point_and_line(X1,line_connecting(esk3_0,esk2_0))
    | apart_point_and_line(X3,X2)
    | apart_point_and_line(X3,line_connecting(esk3_0,esk2_0))
    | apart_point_and_line(esk1_0,X2)
    | ~ distinct_points(X3,X1) ),
    inference(spm,[status(thm)],[21,50,theory(equality)]) ).

cnf(121,negated_conjecture,
    ( distinct_points(esk2_0,X1)
    | distinct_points(X1,esk3_0) ),
    inference(spm,[status(thm)],[29,62,theory(equality)]) ).

cnf(130,negated_conjecture,
    ( distinct_points(X1,X2)
    | distinct_points(esk2_0,X2)
    | distinct_points(X1,esk3_0) ),
    inference(spm,[status(thm)],[34,121,theory(equality)]) ).

cnf(217,negated_conjecture,
    ( distinct_points(X1,esk3_0)
    | distinct_points(X1,esk2_0) ),
    inference(spm,[status(thm)],[29,130,theory(equality)]) ).

cnf(228,negated_conjecture,
    distinct_points(esk3_0,esk2_0),
    inference(spm,[status(thm)],[29,217,theory(equality)]) ).

cnf(475,negated_conjecture,
    ( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk2_0))
    | apart_point_and_line(esk3_0,line_connecting(esk3_0,esk2_0))
    | apart_point_and_line(esk1_0,X1)
    | apart_point_and_line(esk2_0,X1)
    | apart_point_and_line(esk3_0,X1) ),
    inference(spm,[status(thm)],[96,43,theory(equality)]) ).

cnf(2791,negated_conjecture,
    ( distinct_points(esk3_0,esk3_0)
    | apart_point_and_line(esk2_0,line_connecting(esk3_0,esk2_0))
    | apart_point_and_line(esk3_0,X1)
    | apart_point_and_line(esk2_0,X1)
    | apart_point_and_line(esk1_0,X1)
    | ~ distinct_points(esk3_0,esk2_0) ),
    inference(spm,[status(thm)],[18,475,theory(equality)]) ).

cnf(2798,negated_conjecture,
    ( distinct_points(esk3_0,esk3_0)
    | apart_point_and_line(esk2_0,line_connecting(esk3_0,esk2_0))
    | apart_point_and_line(esk3_0,X1)
    | apart_point_and_line(esk2_0,X1)
    | apart_point_and_line(esk1_0,X1)
    | $false ),
    inference(rw,[status(thm)],[2791,228,theory(equality)]) ).

cnf(2799,negated_conjecture,
    ( distinct_points(esk3_0,esk3_0)
    | apart_point_and_line(esk2_0,line_connecting(esk3_0,esk2_0))
    | apart_point_and_line(esk3_0,X1)
    | apart_point_and_line(esk2_0,X1)
    | apart_point_and_line(esk1_0,X1) ),
    inference(cn,[status(thm)],[2798,theory(equality)]) ).

cnf(2800,negated_conjecture,
    ( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk2_0))
    | apart_point_and_line(esk3_0,X1)
    | apart_point_and_line(esk2_0,X1)
    | apart_point_and_line(esk1_0,X1) ),
    inference(sr,[status(thm)],[2799,29,theory(equality)]) ).

cnf(2862,negated_conjecture,
    ( distinct_points(esk2_0,esk2_0)
    | apart_point_and_line(esk1_0,X1)
    | apart_point_and_line(esk2_0,X1)
    | apart_point_and_line(esk3_0,X1)
    | ~ distinct_points(esk3_0,esk2_0) ),
    inference(spm,[status(thm)],[17,2800,theory(equality)]) ).

cnf(2866,negated_conjecture,
    ( distinct_points(esk2_0,esk2_0)
    | apart_point_and_line(esk1_0,X1)
    | apart_point_and_line(esk2_0,X1)
    | apart_point_and_line(esk3_0,X1)
    | $false ),
    inference(rw,[status(thm)],[2862,228,theory(equality)]) ).

cnf(2867,negated_conjecture,
    ( distinct_points(esk2_0,esk2_0)
    | apart_point_and_line(esk1_0,X1)
    | apart_point_and_line(esk2_0,X1)
    | apart_point_and_line(esk3_0,X1) ),
    inference(cn,[status(thm)],[2866,theory(equality)]) ).

cnf(2868,negated_conjecture,
    ( apart_point_and_line(esk1_0,X1)
    | apart_point_and_line(esk2_0,X1)
    | apart_point_and_line(esk3_0,X1) ),
    inference(sr,[status(thm)],[2867,29,theory(equality)]) ).

cnf(2872,negated_conjecture,
    ( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[42,2868,theory(equality)]) ).

cnf(2880,negated_conjecture,
    ( distinct_points(esk1_0,esk1_0)
    | apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
    | ~ distinct_points(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[18,2872,theory(equality)]) ).

cnf(2884,negated_conjecture,
    ( distinct_points(esk1_0,esk1_0)
    | apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[2880,45,theory(equality)]) ).

cnf(2885,negated_conjecture,
    ( distinct_points(esk1_0,esk1_0)
    | apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)) ),
    inference(cn,[status(thm)],[2884,theory(equality)]) ).

cnf(2886,negated_conjecture,
    apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)),
    inference(sr,[status(thm)],[2885,29,theory(equality)]) ).

cnf(2889,negated_conjecture,
    ( distinct_points(esk2_0,esk2_0)
    | ~ distinct_points(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[17,2886,theory(equality)]) ).

cnf(2892,negated_conjecture,
    ( distinct_points(esk2_0,esk2_0)
    | $false ),
    inference(rw,[status(thm)],[2889,45,theory(equality)]) ).

cnf(2893,negated_conjecture,
    distinct_points(esk2_0,esk2_0),
    inference(cn,[status(thm)],[2892,theory(equality)]) ).

cnf(2894,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[2893,29,theory(equality)]) ).

cnf(2895,negated_conjecture,
    $false,
    2894,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO188+2.p
% --creating new selector for [GEO008+0.ax]
% -running prover on /tmp/tmpUn3CFE/sel_GEO188+2.p_1 with time limit 29
% -prover status Theorem
% Problem GEO188+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO188+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO188+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
% 
%------------------------------------------------------------------------------