TSTP Solution File: GEO223+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO223+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.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 08:59:43 EST 2010

% Result   : Theorem 2.03s
% Output   : CNFRefutation 2.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   62 (  33 unt;   0 def)
%            Number of atoms       :  145 (   0 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  129 (  46   ~;  70   |;  10   &)
%                                         (   0 <=>;   3  =>;   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    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  133 (  15 sgn  70   !;   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/tmpgrg9ON/sel_GEO223+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/tmpgrg9ON/sel_GEO223+2.p_1',ouo1) ).

fof(5,axiom,
    ! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
    file('/tmp/tmpgrg9ON/sel_GEO223+2.p_1',ooc1) ).

fof(6,axiom,
    ! [X4,X1] : ~ apart_point_and_line(X4,orthogonal_through_point(X1,X4)),
    file('/tmp/tmpgrg9ON/sel_GEO223+2.p_1',ooc2) ).

fof(7,axiom,
    ! [X5,X6] : ~ apart_point_and_line(X5,parallel_through_point(X6,X5)),
    file('/tmp/tmpgrg9ON/sel_GEO223+2.p_1',cp2) ).

fof(8,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
      | unorthogonal_lines(X1,X2) ),
    file('/tmp/tmpgrg9ON/sel_GEO223+2.p_1',occu1) ).

fof(9,axiom,
    ! [X5,X6] : ~ convergent_lines(parallel_through_point(X6,X5),X6),
    file('/tmp/tmpgrg9ON/sel_GEO223+2.p_1',cp1) ).

fof(12,axiom,
    ! [X5] : ~ convergent_lines(X5,X5),
    file('/tmp/tmpgrg9ON/sel_GEO223+2.p_1',apart3) ).

fof(14,axiom,
    ! [X5,X6,X7] :
      ( convergent_lines(X5,X6)
     => ( convergent_lines(X5,X7)
        | convergent_lines(X6,X7) ) ),
    file('/tmp/tmpgrg9ON/sel_GEO223+2.p_1',apart6) ).

fof(15,conjecture,
    ! [X4,X1] : ~ distinct_lines(parallel_through_point(X1,X4),orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
    file('/tmp/tmpgrg9ON/sel_GEO223+2.p_1',con) ).

fof(16,negated_conjecture,
    ~ ! [X4,X1] : ~ distinct_lines(parallel_through_point(X1,X4),orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
    inference(assume_negation,[status(cth)],[15]) ).

fof(17,plain,
    ! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
    inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).

fof(18,plain,
    ! [X4,X1] : ~ apart_point_and_line(X4,orthogonal_through_point(X1,X4)),
    inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).

fof(19,plain,
    ! [X5,X6] : ~ apart_point_and_line(X5,parallel_through_point(X6,X5)),
    inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).

fof(20,plain,
    ! [X5,X6] : ~ convergent_lines(parallel_through_point(X6,X5),X6),
    inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).

fof(22,plain,
    ! [X5] : ~ convergent_lines(X5,X5),
    inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).

fof(23,negated_conjecture,
    ~ ! [X4,X1] : ~ distinct_lines(parallel_through_point(X1,X4),orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
    inference(fof_simplification,[status(thm)],[16,theory(equality)]) ).

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

fof(26,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)],[25]) ).

cnf(29,plain,
    ( convergent_lines(X1,X3)
    | unorthogonal_lines(X2,X3)
    | ~ unorthogonal_lines(X1,X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(31,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(32,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)],[31]) ).

cnf(33,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)],[32]) ).

fof(40,plain,
    ! [X5,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X5),X6),
    inference(variable_rename,[status(thm)],[17]) ).

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

fof(42,plain,
    ! [X5,X6] : ~ apart_point_and_line(X5,orthogonal_through_point(X6,X5)),
    inference(variable_rename,[status(thm)],[18]) ).

cnf(43,plain,
    ~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
    inference(split_conjunct,[status(thm)],[42]) ).

fof(44,plain,
    ! [X7,X8] : ~ apart_point_and_line(X7,parallel_through_point(X8,X7)),
    inference(variable_rename,[status(thm)],[19]) ).

cnf(45,plain,
    ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
    inference(split_conjunct,[status(thm)],[44]) ).

fof(46,plain,
    ! [X3,X4] :
      ( convergent_lines(X3,X4)
      | unorthogonal_lines(X3,X4) ),
    inference(variable_rename,[status(thm)],[8]) ).

cnf(47,plain,
    ( unorthogonal_lines(X1,X2)
    | convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[46]) ).

fof(48,plain,
    ! [X7,X8] : ~ convergent_lines(parallel_through_point(X8,X7),X8),
    inference(variable_rename,[status(thm)],[20]) ).

cnf(49,plain,
    ~ convergent_lines(parallel_through_point(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[48]) ).

fof(55,plain,
    ! [X6] : ~ convergent_lines(X6,X6),
    inference(variable_rename,[status(thm)],[22]) ).

cnf(56,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[55]) ).

fof(60,plain,
    ! [X5,X6,X7] :
      ( ~ convergent_lines(X5,X6)
      | convergent_lines(X5,X7)
      | convergent_lines(X6,X7) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(61,plain,
    ! [X8,X9,X10] :
      ( ~ convergent_lines(X8,X9)
      | convergent_lines(X8,X10)
      | convergent_lines(X9,X10) ),
    inference(variable_rename,[status(thm)],[60]) ).

cnf(62,plain,
    ( convergent_lines(X1,X2)
    | convergent_lines(X3,X2)
    | ~ convergent_lines(X3,X1) ),
    inference(split_conjunct,[status(thm)],[61]) ).

fof(63,negated_conjecture,
    ? [X4,X1] : distinct_lines(parallel_through_point(X1,X4),orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(64,negated_conjecture,
    ? [X5,X6] : distinct_lines(parallel_through_point(X6,X5),orthogonal_through_point(orthogonal_through_point(X6,X5),X5)),
    inference(variable_rename,[status(thm)],[63]) ).

fof(65,negated_conjecture,
    distinct_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
    inference(skolemize,[status(esa)],[64]) ).

cnf(66,negated_conjecture,
    distinct_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
    inference(split_conjunct,[status(thm)],[65]) ).

cnf(70,plain,
    convergent_lines(orthogonal_through_point(X1,X2),X1),
    inference(spm,[status(thm)],[41,47,theory(equality)]) ).

cnf(77,negated_conjecture,
    ( apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
    | apart_point_and_line(X1,parallel_through_point(esk2_0,esk1_0))
    | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X2)
    | unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),X2) ),
    inference(spm,[status(thm)],[33,66,theory(equality)]) ).

cnf(79,plain,
    ( convergent_lines(X1,X2)
    | convergent_lines(orthogonal_through_point(X1,X3),X2) ),
    inference(spm,[status(thm)],[62,70,theory(equality)]) ).

cnf(81,plain,
    ( convergent_lines(X1,X2)
    | convergent_lines(orthogonal_through_point(X3,X4),X2)
    | convergent_lines(X3,X1) ),
    inference(spm,[status(thm)],[62,79,theory(equality)]) ).

cnf(167,negated_conjecture,
    ( apart_point_and_line(esk1_0,parallel_through_point(esk2_0,esk1_0))
    | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
    inference(spm,[status(thm)],[43,77,theory(equality)]) ).

cnf(173,negated_conjecture,
    ( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
    inference(sr,[status(thm)],[167,45,theory(equality)]) ).

cnf(251,plain,
    ( convergent_lines(X1,X2)
    | convergent_lines(X3,X2)
    | convergent_lines(orthogonal_through_point(X4,X5),X1)
    | convergent_lines(X4,X3) ),
    inference(spm,[status(thm)],[62,81,theory(equality)]) ).

cnf(870,negated_conjecture,
    unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0)),
    inference(spm,[status(thm)],[41,173,theory(equality)]) ).

cnf(875,negated_conjecture,
    ( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
    | convergent_lines(parallel_through_point(esk2_0,esk1_0),X1)
    | ~ convergent_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0)) ),
    inference(spm,[status(thm)],[29,870,theory(equality)]) ).

cnf(3807,plain,
    ( convergent_lines(orthogonal_through_point(X12,X13),X14)
    | convergent_lines(X12,X12)
    | convergent_lines(X14,X12) ),
    inference(ef,[status(thm)],[251,theory(equality)]) ).

cnf(3837,plain,
    ( convergent_lines(orthogonal_through_point(X12,X13),X14)
    | convergent_lines(X14,X12) ),
    inference(sr,[status(thm)],[3807,56,theory(equality)]) ).

cnf(3847,plain,
    ( convergent_lines(X1,X2)
    | convergent_lines(orthogonal_through_point(X3,X4),X2)
    | convergent_lines(X1,X3) ),
    inference(spm,[status(thm)],[62,3837,theory(equality)]) ).

cnf(3884,plain,
    ( convergent_lines(orthogonal_through_point(X1,X3),X4)
    | convergent_lines(parallel_through_point(X1,X2),X4) ),
    inference(spm,[status(thm)],[49,3847,theory(equality)]) ).

cnf(4223,plain,
    convergent_lines(parallel_through_point(X1,X3),orthogonal_through_point(X1,X2)),
    inference(spm,[status(thm)],[56,3884,theory(equality)]) ).

cnf(27635,negated_conjecture,
    ( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
    | convergent_lines(parallel_through_point(esk2_0,esk1_0),X1)
    | $false ),
    inference(rw,[status(thm)],[875,4223,theory(equality)]) ).

cnf(27636,negated_conjecture,
    ( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
    | convergent_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
    inference(cn,[status(thm)],[27635,theory(equality)]) ).

cnf(27637,negated_conjecture,
    convergent_lines(parallel_through_point(esk2_0,esk1_0),esk2_0),
    inference(spm,[status(thm)],[41,27636,theory(equality)]) ).

cnf(27641,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[27637,49,theory(equality)]) ).

cnf(27642,negated_conjecture,
    $false,
    27641,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO223+2.p
% --creating new selector for [GEO008+0.ax, GEO006+2.ax, GEO006+3.ax]
% -running prover on /tmp/tmpgrg9ON/sel_GEO223+2.p_1 with time limit 29
% -prover status Theorem
% Problem GEO223+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO223+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO223+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
% 
%------------------------------------------------------------------------------