TSTP Solution File: GEO175+3 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO175+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 08:44:39 EST 2010

% Result   : Theorem 0.24s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   44 (  11 unt;   0 def)
%            Number of atoms       :  128 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  125 (  41   ~;  59   |;  17   &)
%                                         (   0 <=>;   8  =>;   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    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   77 (   0 sgn  48   !;   8   ?)

% 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/tmp7KVsLX/sel_GEO175+3.p_1',cu1) ).

fof(5,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( distinct_lines(X2,X3)
        | convergent_lines(X1,X3) ) ),
    file('/tmp/tmp7KVsLX/sel_GEO175+3.p_1',ceq3) ).

fof(8,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    file('/tmp/tmp7KVsLX/sel_GEO175+3.p_1',ci3) ).

fof(10,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    file('/tmp/tmp7KVsLX/sel_GEO175+3.p_1',ci4) ).

fof(13,axiom,
    ! [X1] : ~ convergent_lines(X1,X1),
    file('/tmp/tmp7KVsLX/sel_GEO175+3.p_1',apart3) ).

fof(16,conjecture,
    ! [X1,X2,X4,X5] :
      ( ( distinct_points(X1,X2)
        & convergent_lines(X4,X5)
        & distinct_points(X1,intersection_point(X4,X5)) )
     => ( apart_point_and_line(X1,X4)
        | apart_point_and_line(X1,X5) ) ),
    file('/tmp/tmp7KVsLX/sel_GEO175+3.p_1',con) ).

fof(17,negated_conjecture,
    ~ ! [X1,X2,X4,X5] :
        ( ( distinct_points(X1,X2)
          & convergent_lines(X4,X5)
          & distinct_points(X1,intersection_point(X4,X5)) )
       => ( apart_point_and_line(X1,X4)
          | apart_point_and_line(X1,X5) ) ),
    inference(assume_negation,[status(cth)],[16]) ).

fof(19,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).

fof(20,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).

fof(22,plain,
    ! [X1] : ~ convergent_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[13,theory(equality)]) ).

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

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

fof(34,plain,
    ! [X1,X2,X3] :
      ( ~ convergent_lines(X1,X2)
      | distinct_lines(X2,X3)
      | convergent_lines(X1,X3) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(35,plain,
    ! [X4,X5,X6] :
      ( ~ convergent_lines(X4,X5)
      | distinct_lines(X5,X6)
      | convergent_lines(X4,X6) ),
    inference(variable_rename,[status(thm)],[34]) ).

cnf(36,plain,
    ( convergent_lines(X1,X2)
    | distinct_lines(X3,X2)
    | ~ convergent_lines(X1,X3) ),
    inference(split_conjunct,[status(thm)],[35]) ).

fof(43,plain,
    ! [X1,X2] :
      ( ~ convergent_lines(X1,X2)
      | ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(44,plain,
    ! [X3,X4] :
      ( ~ convergent_lines(X3,X4)
      | ~ apart_point_and_line(intersection_point(X3,X4),X3) ),
    inference(variable_rename,[status(thm)],[43]) ).

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

fof(49,plain,
    ! [X1,X2] :
      ( ~ convergent_lines(X1,X2)
      | ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(50,plain,
    ! [X3,X4] :
      ( ~ convergent_lines(X3,X4)
      | ~ apart_point_and_line(intersection_point(X3,X4),X4) ),
    inference(variable_rename,[status(thm)],[49]) ).

cnf(51,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[50]) ).

fof(57,plain,
    ! [X2] : ~ convergent_lines(X2,X2),
    inference(variable_rename,[status(thm)],[22]) ).

cnf(58,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[57]) ).

fof(65,negated_conjecture,
    ? [X1,X2,X4,X5] :
      ( distinct_points(X1,X2)
      & convergent_lines(X4,X5)
      & distinct_points(X1,intersection_point(X4,X5))
      & ~ apart_point_and_line(X1,X4)
      & ~ apart_point_and_line(X1,X5) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(66,negated_conjecture,
    ? [X6,X7,X8,X9] :
      ( distinct_points(X6,X7)
      & convergent_lines(X8,X9)
      & distinct_points(X6,intersection_point(X8,X9))
      & ~ apart_point_and_line(X6,X8)
      & ~ apart_point_and_line(X6,X9) ),
    inference(variable_rename,[status(thm)],[65]) ).

fof(67,negated_conjecture,
    ( distinct_points(esk1_0,esk2_0)
    & convergent_lines(esk3_0,esk4_0)
    & distinct_points(esk1_0,intersection_point(esk3_0,esk4_0))
    & ~ apart_point_and_line(esk1_0,esk3_0)
    & ~ apart_point_and_line(esk1_0,esk4_0) ),
    inference(skolemize,[status(esa)],[66]) ).

cnf(68,negated_conjecture,
    ~ apart_point_and_line(esk1_0,esk4_0),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(69,negated_conjecture,
    ~ apart_point_and_line(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(70,negated_conjecture,
    distinct_points(esk1_0,intersection_point(esk3_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(71,negated_conjecture,
    convergent_lines(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(76,negated_conjecture,
    ( convergent_lines(esk3_0,X1)
    | distinct_lines(esk4_0,X1) ),
    inference(spm,[status(thm)],[36,71,theory(equality)]) ).

cnf(92,negated_conjecture,
    ( apart_point_and_line(X1,X2)
    | apart_point_and_line(X1,esk4_0)
    | apart_point_and_line(X3,X2)
    | apart_point_and_line(X3,esk4_0)
    | convergent_lines(esk3_0,X2)
    | ~ distinct_points(X3,X1) ),
    inference(spm,[status(thm)],[33,76,theory(equality)]) ).

cnf(224,negated_conjecture,
    ( apart_point_and_line(esk1_0,esk4_0)
    | apart_point_and_line(intersection_point(esk3_0,esk4_0),esk4_0)
    | apart_point_and_line(esk1_0,X1)
    | apart_point_and_line(intersection_point(esk3_0,esk4_0),X1)
    | convergent_lines(esk3_0,X1) ),
    inference(spm,[status(thm)],[92,70,theory(equality)]) ).

cnf(246,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk4_0)
    | apart_point_and_line(esk1_0,X1)
    | apart_point_and_line(intersection_point(esk3_0,esk4_0),X1)
    | convergent_lines(esk3_0,X1) ),
    inference(sr,[status(thm)],[224,68,theory(equality)]) ).

cnf(951,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk3_0,esk4_0),X1)
    | apart_point_and_line(esk1_0,X1)
    | convergent_lines(esk3_0,X1)
    | ~ convergent_lines(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[51,246,theory(equality)]) ).

cnf(958,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk3_0,esk4_0),X1)
    | apart_point_and_line(esk1_0,X1)
    | convergent_lines(esk3_0,X1)
    | $false ),
    inference(rw,[status(thm)],[951,71,theory(equality)]) ).

cnf(959,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk3_0,esk4_0),X1)
    | apart_point_and_line(esk1_0,X1)
    | convergent_lines(esk3_0,X1) ),
    inference(cn,[status(thm)],[958,theory(equality)]) ).

cnf(961,negated_conjecture,
    ( apart_point_and_line(esk1_0,esk3_0)
    | convergent_lines(esk3_0,esk3_0)
    | ~ convergent_lines(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[45,959,theory(equality)]) ).

cnf(967,negated_conjecture,
    ( apart_point_and_line(esk1_0,esk3_0)
    | convergent_lines(esk3_0,esk3_0)
    | $false ),
    inference(rw,[status(thm)],[961,71,theory(equality)]) ).

cnf(968,negated_conjecture,
    ( apart_point_and_line(esk1_0,esk3_0)
    | convergent_lines(esk3_0,esk3_0) ),
    inference(cn,[status(thm)],[967,theory(equality)]) ).

cnf(969,negated_conjecture,
    convergent_lines(esk3_0,esk3_0),
    inference(sr,[status(thm)],[968,69,theory(equality)]) ).

cnf(970,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[969,58,theory(equality)]) ).

cnf(971,negated_conjecture,
    $false,
    970,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO175+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/tmp7KVsLX/sel_GEO175+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO175+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO175+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO175+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
% 
%------------------------------------------------------------------------------