TSTP Solution File: GEO222+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO222+2 : TPTP v5.0.0. Released v3.3.0.
% 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 08:59:29 EST 2010

% Result   : Theorem 9.77s
% Output   : CNFRefutation 9.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   77 (  29 unt;   0 def)
%            Number of atoms       :  202 (   0 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  178 (  53   ~; 110   |;  10   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :  162 (  21 sgn  76   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] :
      ( ( convergent_lines(X1,X2)
        & unorthogonal_lines(X1,X2) )
     => ( ( convergent_lines(X1,X3)
          & unorthogonal_lines(X1,X3) )
        | ( convergent_lines(X2,X3)
          & unorthogonal_lines(X2,X3) ) ) ),
    file('/tmp/tmpHzTdZ4/sel_GEO222+2.p_1',oac1) ).

fof(2,axiom,
    ! [X4,X1,X2,X3] :
      ( distinct_lines(X1,X2)
     => ( apart_point_and_line(X4,X1)
        | apart_point_and_line(X4,X2)
        | unorthogonal_lines(X1,X3)
        | unorthogonal_lines(X2,X3) ) ),
    file('/tmp/tmpHzTdZ4/sel_GEO222+2.p_1',ouo1) ).

fof(3,axiom,
    ! [X5,X6] :
      ( convergent_lines(X5,X6)
     => distinct_lines(X5,X6) ),
    file('/tmp/tmpHzTdZ4/sel_GEO222+2.p_1',ceq3) ).

fof(5,axiom,
    ! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
    file('/tmp/tmpHzTdZ4/sel_GEO222+2.p_1',ooc1) ).

fof(6,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
      | unorthogonal_lines(X1,X2) ),
    file('/tmp/tmpHzTdZ4/sel_GEO222+2.p_1',occu1) ).

fof(7,axiom,
    ! [X4,X1] : ~ apart_point_and_line(X4,orthogonal_through_point(X1,X4)),
    file('/tmp/tmpHzTdZ4/sel_GEO222+2.p_1',ooc2) ).

fof(9,axiom,
    ! [X5] : ~ distinct_lines(X5,X5),
    file('/tmp/tmpHzTdZ4/sel_GEO222+2.p_1',apart2) ).

fof(10,axiom,
    ! [X5] : ~ convergent_lines(X5,X5),
    file('/tmp/tmpHzTdZ4/sel_GEO222+2.p_1',apart3) ).

fof(11,axiom,
    ! [X5,X6,X7] :
      ( distinct_lines(X5,X6)
     => ( distinct_lines(X5,X7)
        | distinct_lines(X6,X7) ) ),
    file('/tmp/tmpHzTdZ4/sel_GEO222+2.p_1',apart5) ).

fof(12,axiom,
    ! [X5,X6,X7] :
      ( convergent_lines(X5,X6)
     => ( convergent_lines(X5,X7)
        | convergent_lines(X6,X7) ) ),
    file('/tmp/tmpHzTdZ4/sel_GEO222+2.p_1',apart6) ).

fof(13,conjecture,
    ! [X4,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
    file('/tmp/tmpHzTdZ4/sel_GEO222+2.p_1',con) ).

fof(14,negated_conjecture,
    ~ ! [X4,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
    inference(assume_negation,[status(cth)],[13]) ).

fof(15,plain,
    ! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
    inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).

fof(16,plain,
    ! [X4,X1] : ~ apart_point_and_line(X4,orthogonal_through_point(X1,X4)),
    inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).

fof(17,plain,
    ! [X5] : ~ distinct_lines(X5,X5),
    inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).

fof(18,plain,
    ! [X5] : ~ convergent_lines(X5,X5),
    inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).

fof(19,negated_conjecture,
    ~ ! [X4,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
    inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).

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

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

fof(22,plain,
    ! [X4,X5,X6] :
      ( ( convergent_lines(X5,X6)
        | convergent_lines(X4,X6)
        | ~ convergent_lines(X4,X5)
        | ~ unorthogonal_lines(X4,X5) )
      & ( unorthogonal_lines(X5,X6)
        | convergent_lines(X4,X6)
        | ~ convergent_lines(X4,X5)
        | ~ unorthogonal_lines(X4,X5) )
      & ( convergent_lines(X5,X6)
        | unorthogonal_lines(X4,X6)
        | ~ convergent_lines(X4,X5)
        | ~ unorthogonal_lines(X4,X5) )
      & ( unorthogonal_lines(X5,X6)
        | unorthogonal_lines(X4,X6)
        | ~ convergent_lines(X4,X5)
        | ~ unorthogonal_lines(X4,X5) ) ),
    inference(distribute,[status(thm)],[21]) ).

cnf(23,plain,
    ( unorthogonal_lines(X1,X3)
    | unorthogonal_lines(X2,X3)
    | ~ unorthogonal_lines(X1,X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(25,plain,
    ( convergent_lines(X1,X3)
    | unorthogonal_lines(X2,X3)
    | ~ unorthogonal_lines(X1,X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[22]) ).

fof(27,plain,
    ! [X4,X1,X2,X3] :
      ( ~ distinct_lines(X1,X2)
      | apart_point_and_line(X4,X1)
      | apart_point_and_line(X4,X2)
      | unorthogonal_lines(X1,X3)
      | unorthogonal_lines(X2,X3) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(28,plain,
    ! [X5,X6,X7,X8] :
      ( ~ distinct_lines(X6,X7)
      | apart_point_and_line(X5,X6)
      | apart_point_and_line(X5,X7)
      | unorthogonal_lines(X6,X8)
      | unorthogonal_lines(X7,X8) ),
    inference(variable_rename,[status(thm)],[27]) ).

cnf(29,plain,
    ( unorthogonal_lines(X1,X2)
    | unorthogonal_lines(X3,X2)
    | apart_point_and_line(X4,X1)
    | apart_point_and_line(X4,X3)
    | ~ distinct_lines(X3,X1) ),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(30,plain,
    ! [X5,X6] :
      ( ~ convergent_lines(X5,X6)
      | distinct_lines(X5,X6) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(31,plain,
    ! [X7,X8] :
      ( ~ convergent_lines(X7,X8)
      | distinct_lines(X7,X8) ),
    inference(variable_rename,[status(thm)],[30]) ).

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

fof(36,plain,
    ! [X5,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X5),X6),
    inference(variable_rename,[status(thm)],[15]) ).

cnf(37,plain,
    ~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[36]) ).

fof(38,plain,
    ! [X3,X4] :
      ( convergent_lines(X3,X4)
      | unorthogonal_lines(X3,X4) ),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(39,plain,
    ( unorthogonal_lines(X1,X2)
    | convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[38]) ).

fof(40,plain,
    ! [X5,X6] : ~ apart_point_and_line(X5,orthogonal_through_point(X6,X5)),
    inference(variable_rename,[status(thm)],[16]) ).

cnf(41,plain,
    ~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
    inference(split_conjunct,[status(thm)],[40]) ).

fof(45,plain,
    ! [X6] : ~ distinct_lines(X6,X6),
    inference(variable_rename,[status(thm)],[17]) ).

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

fof(47,plain,
    ! [X6] : ~ convergent_lines(X6,X6),
    inference(variable_rename,[status(thm)],[18]) ).

cnf(48,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[47]) ).

fof(49,plain,
    ! [X5,X6,X7] :
      ( ~ distinct_lines(X5,X6)
      | distinct_lines(X5,X7)
      | distinct_lines(X6,X7) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(50,plain,
    ! [X8,X9,X10] :
      ( ~ distinct_lines(X8,X9)
      | distinct_lines(X8,X10)
      | distinct_lines(X9,X10) ),
    inference(variable_rename,[status(thm)],[49]) ).

cnf(51,plain,
    ( distinct_lines(X1,X2)
    | distinct_lines(X3,X2)
    | ~ distinct_lines(X3,X1) ),
    inference(split_conjunct,[status(thm)],[50]) ).

fof(52,plain,
    ! [X5,X6,X7] :
      ( ~ convergent_lines(X5,X6)
      | convergent_lines(X5,X7)
      | convergent_lines(X6,X7) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(53,plain,
    ! [X8,X9,X10] :
      ( ~ convergent_lines(X8,X9)
      | convergent_lines(X8,X10)
      | convergent_lines(X9,X10) ),
    inference(variable_rename,[status(thm)],[52]) ).

cnf(54,plain,
    ( convergent_lines(X1,X2)
    | convergent_lines(X3,X2)
    | ~ convergent_lines(X3,X1) ),
    inference(split_conjunct,[status(thm)],[53]) ).

fof(55,negated_conjecture,
    ? [X4,X1] : convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(56,negated_conjecture,
    ? [X5,X6] : convergent_lines(X6,orthogonal_through_point(orthogonal_through_point(X6,X5),X5)),
    inference(variable_rename,[status(thm)],[55]) ).

fof(57,negated_conjecture,
    convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
    inference(skolemize,[status(esa)],[56]) ).

cnf(58,negated_conjecture,
    convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
    inference(split_conjunct,[status(thm)],[57]) ).

cnf(59,plain,
    convergent_lines(orthogonal_through_point(X1,X2),X1),
    inference(spm,[status(thm)],[37,39,theory(equality)]) ).

cnf(61,negated_conjecture,
    ( convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | convergent_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[54,58,theory(equality)]) ).

cnf(62,plain,
    ( distinct_lines(X1,X2)
    | distinct_lines(X3,X2)
    | ~ convergent_lines(X3,X1) ),
    inference(spm,[status(thm)],[51,32,theory(equality)]) ).

cnf(69,plain,
    ( convergent_lines(X1,X2)
    | convergent_lines(orthogonal_through_point(X1,X3),X2) ),
    inference(spm,[status(thm)],[54,59,theory(equality)]) ).

cnf(70,plain,
    convergent_lines(X1,orthogonal_through_point(X1,X2)),
    inference(spm,[status(thm)],[48,69,theory(equality)]) ).

cnf(84,negated_conjecture,
    ( convergent_lines(X1,X2)
    | convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X2)
    | convergent_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[54,61,theory(equality)]) ).

cnf(92,negated_conjecture,
    ( convergent_lines(X1,X2)
    | convergent_lines(X3,X2)
    | convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | convergent_lines(esk2_0,X3) ),
    inference(spm,[status(thm)],[54,84,theory(equality)]) ).

cnf(102,plain,
    ( distinct_lines(orthogonal_through_point(X1,X2),X3)
    | distinct_lines(X1,X3) ),
    inference(spm,[status(thm)],[62,59,theory(equality)]) ).

cnf(114,plain,
    distinct_lines(X1,orthogonal_through_point(X1,X2)),
    inference(spm,[status(thm)],[46,102,theory(equality)]) ).

cnf(120,plain,
    ( apart_point_and_line(X1,orthogonal_through_point(X2,X3))
    | apart_point_and_line(X1,X2)
    | unorthogonal_lines(orthogonal_through_point(X2,X3),X4)
    | unorthogonal_lines(X2,X4) ),
    inference(spm,[status(thm)],[29,114,theory(equality)]) ).

cnf(404,negated_conjecture,
    ( convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),esk2_0)
    | convergent_lines(X6,X6)
    | convergent_lines(esk2_0,X6) ),
    inference(ef,[status(thm)],[92,theory(equality)]) ).

cnf(428,negated_conjecture,
    ( convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),esk2_0)
    | convergent_lines(esk2_0,X6) ),
    inference(sr,[status(thm)],[404,48,theory(equality)]) ).

cnf(814,plain,
    ( apart_point_and_line(X1,X2)
    | unorthogonal_lines(orthogonal_through_point(X2,X1),X3)
    | unorthogonal_lines(X2,X3) ),
    inference(spm,[status(thm)],[41,120,theory(equality)]) ).

cnf(1740,plain,
    ( unorthogonal_lines(X1,X2)
    | convergent_lines(orthogonal_through_point(X3,X4),X2)
    | apart_point_and_line(X4,X3)
    | unorthogonal_lines(X3,X1)
    | ~ convergent_lines(orthogonal_through_point(X3,X4),X1) ),
    inference(spm,[status(thm)],[25,814,theory(equality)]) ).

cnf(140702,negated_conjecture,
    ( apart_point_and_line(esk1_0,orthogonal_through_point(esk2_0,esk1_0))
    | unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),esk2_0)
    | unorthogonal_lines(esk2_0,X1)
    | convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | convergent_lines(esk2_0,X2) ),
    inference(spm,[status(thm)],[1740,428,theory(equality)]) ).

cnf(142424,negated_conjecture,
    ( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),esk2_0)
    | unorthogonal_lines(esk2_0,X1)
    | convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | convergent_lines(esk2_0,X2) ),
    inference(sr,[status(thm)],[140702,41,theory(equality)]) ).

cnf(142425,negated_conjecture,
    ( unorthogonal_lines(esk2_0,X1)
    | convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | convergent_lines(esk2_0,X2) ),
    inference(sr,[status(thm)],[142424,37,theory(equality)]) ).

cnf(142563,negated_conjecture,
    ( unorthogonal_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
    | convergent_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[48,142425,theory(equality)]) ).

cnf(142687,negated_conjecture,
    ( unorthogonal_lines(esk2_0,X1)
    | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | convergent_lines(esk2_0,X2)
    | ~ convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)) ),
    inference(spm,[status(thm)],[23,142563,theory(equality)]) ).

cnf(142734,negated_conjecture,
    ( unorthogonal_lines(esk2_0,X1)
    | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | convergent_lines(esk2_0,X2)
    | $false ),
    inference(rw,[status(thm)],[142687,58,theory(equality)]) ).

cnf(142735,negated_conjecture,
    ( unorthogonal_lines(esk2_0,X1)
    | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | convergent_lines(esk2_0,X2) ),
    inference(cn,[status(thm)],[142734,theory(equality)]) ).

cnf(144700,negated_conjecture,
    ( unorthogonal_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0))
    | convergent_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[37,142735,theory(equality)]) ).

cnf(144754,negated_conjecture,
    ( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
    | convergent_lines(esk2_0,X1)
    | convergent_lines(esk2_0,X2)
    | ~ convergent_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0)) ),
    inference(spm,[status(thm)],[25,144700,theory(equality)]) ).

cnf(144800,negated_conjecture,
    ( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
    | convergent_lines(esk2_0,X1)
    | convergent_lines(esk2_0,X2)
    | $false ),
    inference(rw,[status(thm)],[144754,70,theory(equality)]) ).

cnf(144801,negated_conjecture,
    ( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
    | convergent_lines(esk2_0,X1)
    | convergent_lines(esk2_0,X2) ),
    inference(cn,[status(thm)],[144800,theory(equality)]) ).

cnf(144924,negated_conjecture,
    ( convergent_lines(esk2_0,X1)
    | convergent_lines(esk2_0,esk2_0) ),
    inference(spm,[status(thm)],[37,144801,theory(equality)]) ).

cnf(144971,negated_conjecture,
    convergent_lines(esk2_0,X1),
    inference(sr,[status(thm)],[144924,48,theory(equality)]) ).

cnf(144977,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[48,144971,theory(equality)]) ).

cnf(145260,negated_conjecture,
    $false,
    144977,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO222+2.p
% --creating new selector for [GEO008+0.ax, GEO006+2.ax, GEO006+3.ax]
% -running prover on /tmp/tmpHzTdZ4/sel_GEO222+2.p_1 with time limit 29
% -prover status Theorem
% Problem GEO222+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO222+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO222+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
% 
%------------------------------------------------------------------------------