TSTP Solution File: GEO222+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO222+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 08:59:36 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   58 (  21 unt;   0 def)
%            Number of atoms       :  173 (   0 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  194 (  79   ~;  82   |;  25   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :  118 (   5 sgn  77   !;   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/tmpA51HqF/sel_GEO222+3.p_1',oac1) ).

fof(4,axiom,
    ! [X5,X6,X7] :
      ( convergent_lines(X5,X6)
     => ( convergent_lines(X5,X7)
        | convergent_lines(X6,X7) ) ),
    file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',ax6) ).

fof(5,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/tmpA51HqF/sel_GEO222+3.p_1',cotno1) ).

fof(10,axiom,
    ! [X5,X6] :
      ( parallel_lines(X5,X6)
    <=> ~ convergent_lines(X5,X6) ),
    file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',a3) ).

fof(11,axiom,
    ! [X1,X2] :
      ~ ( ~ convergent_lines(X1,X2)
        & ~ unorthogonal_lines(X1,X2) ),
    file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',coipo1) ).

fof(12,axiom,
    ! [X1,X2,X3] :
      ( ( ~ unorthogonal_lines(X1,X2)
        & ~ unorthogonal_lines(X1,X3) )
     => ~ convergent_lines(X2,X3) ),
    file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',couo1) ).

fof(15,axiom,
    ! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
    file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',ooc1) ).

fof(16,axiom,
    ! [X5] : ~ convergent_lines(X5,X5),
    file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',apart3) ).

fof(19,conjecture,
    ! [X4,X1] : parallel_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
    file('/tmp/tmpA51HqF/sel_GEO222+3.p_1',con) ).

fof(20,negated_conjecture,
    ~ ! [X4,X1] : parallel_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
    inference(assume_negation,[status(cth)],[19]) ).

fof(21,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_simplification,[status(thm)],[5,theory(equality)]) ).

fof(22,plain,
    ! [X5,X6] :
      ( parallel_lines(X5,X6)
    <=> ~ convergent_lines(X5,X6) ),
    inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).

fof(23,plain,
    ! [X1,X2] :
      ~ ( ~ convergent_lines(X1,X2)
        & ~ unorthogonal_lines(X1,X2) ),
    inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).

fof(24,plain,
    ! [X1,X2,X3] :
      ( ( ~ unorthogonal_lines(X1,X2)
        & ~ unorthogonal_lines(X1,X3) )
     => ~ convergent_lines(X2,X3) ),
    inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).

fof(26,plain,
    ! [X4,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X4),X1),
    inference(fof_simplification,[status(thm)],[15,theory(equality)]) ).

fof(27,plain,
    ! [X5] : ~ convergent_lines(X5,X5),
    inference(fof_simplification,[status(thm)],[16,theory(equality)]) ).

fof(29,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(30,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)],[29]) ).

fof(31,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)],[30]) ).

cnf(32,plain,
    ( unorthogonal_lines(X1,X3)
    | unorthogonal_lines(X2,X3)
    | ~ unorthogonal_lines(X1,X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[31]) ).

fof(42,plain,
    ! [X5,X6,X7] :
      ( ~ convergent_lines(X5,X6)
      | convergent_lines(X5,X7)
      | convergent_lines(X6,X7) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(43,plain,
    ! [X8,X9,X10] :
      ( ~ convergent_lines(X8,X9)
      | convergent_lines(X8,X10)
      | convergent_lines(X9,X10) ),
    inference(variable_rename,[status(thm)],[42]) ).

cnf(44,plain,
    ( convergent_lines(X1,X2)
    | convergent_lines(X3,X2)
    | ~ convergent_lines(X3,X1) ),
    inference(split_conjunct,[status(thm)],[43]) ).

fof(45,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)],[21]) ).

fof(46,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)],[45]) ).

fof(47,plain,
    ! [X4,X5,X6] :
      ( ( convergent_lines(X4,X6)
        | convergent_lines(X4,X5)
        | ~ convergent_lines(X5,X6)
        | ~ unorthogonal_lines(X5,X6) )
      & ( unorthogonal_lines(X4,X6)
        | convergent_lines(X4,X5)
        | ~ convergent_lines(X5,X6)
        | ~ unorthogonal_lines(X5,X6) )
      & ( convergent_lines(X4,X6)
        | unorthogonal_lines(X4,X5)
        | ~ convergent_lines(X5,X6)
        | ~ unorthogonal_lines(X5,X6) )
      & ( unorthogonal_lines(X4,X6)
        | unorthogonal_lines(X4,X5)
        | ~ convergent_lines(X5,X6)
        | ~ unorthogonal_lines(X5,X6) ) ),
    inference(distribute,[status(thm)],[46]) ).

cnf(49,plain,
    ( unorthogonal_lines(X3,X1)
    | convergent_lines(X3,X2)
    | ~ unorthogonal_lines(X1,X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[47]) ).

fof(64,plain,
    ! [X5,X6] :
      ( ( ~ parallel_lines(X5,X6)
        | ~ convergent_lines(X5,X6) )
      & ( convergent_lines(X5,X6)
        | parallel_lines(X5,X6) ) ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(65,plain,
    ! [X7,X8] :
      ( ( ~ parallel_lines(X7,X8)
        | ~ convergent_lines(X7,X8) )
      & ( convergent_lines(X7,X8)
        | parallel_lines(X7,X8) ) ),
    inference(variable_rename,[status(thm)],[64]) ).

cnf(66,plain,
    ( parallel_lines(X1,X2)
    | convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[65]) ).

fof(68,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
      | unorthogonal_lines(X1,X2) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(69,plain,
    ! [X3,X4] :
      ( convergent_lines(X3,X4)
      | unorthogonal_lines(X3,X4) ),
    inference(variable_rename,[status(thm)],[68]) ).

cnf(70,plain,
    ( unorthogonal_lines(X1,X2)
    | convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[69]) ).

fof(71,plain,
    ! [X1,X2,X3] :
      ( unorthogonal_lines(X1,X2)
      | unorthogonal_lines(X1,X3)
      | ~ convergent_lines(X2,X3) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(72,plain,
    ! [X4,X5,X6] :
      ( unorthogonal_lines(X4,X5)
      | unorthogonal_lines(X4,X6)
      | ~ convergent_lines(X5,X6) ),
    inference(variable_rename,[status(thm)],[71]) ).

cnf(73,plain,
    ( unorthogonal_lines(X3,X2)
    | unorthogonal_lines(X3,X1)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[72]) ).

fof(79,plain,
    ! [X5,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X5),X6),
    inference(variable_rename,[status(thm)],[26]) ).

cnf(80,plain,
    ~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[79]) ).

fof(81,plain,
    ! [X6] : ~ convergent_lines(X6,X6),
    inference(variable_rename,[status(thm)],[27]) ).

cnf(82,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[81]) ).

fof(87,negated_conjecture,
    ? [X4,X1] : ~ parallel_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X4),X4)),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(88,negated_conjecture,
    ? [X5,X6] : ~ parallel_lines(X6,orthogonal_through_point(orthogonal_through_point(X6,X5),X5)),
    inference(variable_rename,[status(thm)],[87]) ).

fof(89,negated_conjecture,
    ~ parallel_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
    inference(skolemize,[status(esa)],[88]) ).

cnf(90,negated_conjecture,
    ~ parallel_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
    inference(split_conjunct,[status(thm)],[89]) ).

cnf(91,plain,
    convergent_lines(orthogonal_through_point(X1,X2),X1),
    inference(spm,[status(thm)],[80,70,theory(equality)]) ).

cnf(92,negated_conjecture,
    convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
    inference(spm,[status(thm)],[90,66,theory(equality)]) ).

cnf(104,plain,
    ( convergent_lines(X1,X2)
    | convergent_lines(orthogonal_through_point(X1,X3),X2) ),
    inference(spm,[status(thm)],[44,91,theory(equality)]) ).

cnf(106,plain,
    ( unorthogonal_lines(X1,orthogonal_through_point(X2,X3))
    | unorthogonal_lines(X1,X2) ),
    inference(spm,[status(thm)],[73,91,theory(equality)]) ).

cnf(110,plain,
    convergent_lines(X1,orthogonal_through_point(X1,X2)),
    inference(spm,[status(thm)],[82,104,theory(equality)]) ).

cnf(141,plain,
    ( unorthogonal_lines(X1,X2)
    | unorthogonal_lines(orthogonal_through_point(X3,X4),X2)
    | unorthogonal_lines(X1,X3)
    | ~ convergent_lines(X1,orthogonal_through_point(X3,X4)) ),
    inference(spm,[status(thm)],[32,106,theory(equality)]) ).

cnf(697,negated_conjecture,
    ( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | unorthogonal_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0))
    | unorthogonal_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[141,92,theory(equality)]) ).

cnf(728,negated_conjecture,
    unorthogonal_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0)),
    inference(spm,[status(thm)],[80,697,theory(equality)]) ).

cnf(736,negated_conjecture,
    ( unorthogonal_lines(X1,esk2_0)
    | convergent_lines(X1,orthogonal_through_point(esk2_0,esk1_0))
    | ~ convergent_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0)) ),
    inference(spm,[status(thm)],[49,728,theory(equality)]) ).

cnf(754,negated_conjecture,
    ( unorthogonal_lines(X1,esk2_0)
    | convergent_lines(X1,orthogonal_through_point(esk2_0,esk1_0))
    | $false ),
    inference(rw,[status(thm)],[736,110,theory(equality)]) ).

cnf(755,negated_conjecture,
    ( unorthogonal_lines(X1,esk2_0)
    | convergent_lines(X1,orthogonal_through_point(esk2_0,esk1_0)) ),
    inference(cn,[status(thm)],[754,theory(equality)]) ).

cnf(775,negated_conjecture,
    unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),esk2_0),
    inference(spm,[status(thm)],[82,755,theory(equality)]) ).

cnf(785,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[775,80,theory(equality)]) ).

cnf(786,negated_conjecture,
    $false,
    785,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO222+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/tmpA51HqF/sel_GEO222+3.p_1 with time limit 29
% -prover status Theorem
% Problem GEO222+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO222+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO222+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
% 
%------------------------------------------------------------------------------