%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GEO011-5 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art02.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 11:52:16 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   13 (  10 unt;   0 def)
%            Number of atoms       :   20 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   15 (   8   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :    6 (   0 sgn   3   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(lower_dimension3,plain,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO011-5.tptp',unknown),
    [] ).

cnf(149677696,plain,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    inference(rewrite,[status(thm)],[lower_dimension3]),
    [] ).

fof(prove_lower_dimension_points_not_colinear,plain,
    colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO011-5.tptp',unknown),
    [] ).

cnf(149686144,plain,
    colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    inference(rewrite,[status(thm)],[prove_lower_dimension_points_not_colinear]),
    [] ).

fof(colinearity4,plain,
    ! [A,B,C] :
      ( ~ colinear(A,B,C)
      | between(A,B,C)
      | between(B,C,A)
      | between(C,A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO011-5.tptp',unknown),
    [] ).

cnf(149566096,plain,
    ( ~ colinear(A,B,C)
    | between(A,B,C)
    | between(B,C,A)
    | between(C,A,B) ),
    inference(rewrite,[status(thm)],[colinearity4]),
    [] ).

fof(lower_dimension1,plain,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO011-5.tptp',unknown),
    [] ).

cnf(149669976,plain,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    inference(rewrite,[status(thm)],[lower_dimension1]),
    [] ).

cnf(157487696,plain,
    ( between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
    | between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[149686144,149566096,149669976]),
    [] ).

fof(lower_dimension2,plain,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO011-5.tptp',unknown),
    [] ).

cnf(149674072,plain,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    inference(rewrite,[status(thm)],[lower_dimension2]),
    [] ).

cnf(157495064,plain,
    between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    inference(resolution,[status(thm)],[157487696,149674072]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[149677696,157495064]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(lower_dimension3,plain,(~between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO011-5.tptp',unknown),[]).
% 
% cnf(149677696,plain,(~between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)),inference(rewrite,[status(thm)],[lower_dimension3]),[]).
% 
% fof(prove_lower_dimension_points_not_colinear,plain,(colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO011-5.tptp',unknown),[]).
% 
% cnf(149686144,plain,(colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)),inference(rewrite,[status(thm)],[prove_lower_dimension_points_not_colinear]),[]).
% 
% fof(colinearity4,plain,(~colinear(A,B,C)|between(A,B,C)|between(B,C,A)|between(C,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO011-5.tptp',unknown),[]).
% 
% cnf(149566096,plain,(~colinear(A,B,C)|between(A,B,C)|between(B,C,A)|between(C,A,B)),inference(rewrite,[status(thm)],[colinearity4]),[]).
% 
% fof(lower_dimension1,plain,(~between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO011-5.tptp',unknown),[]).
% 
% cnf(149669976,plain,(~between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)),inference(rewrite,[status(thm)],[lower_dimension1]),[]).
% 
% cnf(157487696,plain,(between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)|between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[149686144,149566096,149669976]),[]).
% 
% fof(lower_dimension2,plain,(~between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO011-5.tptp',unknown),[]).
% 
% cnf(149674072,plain,(~between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)),inference(rewrite,[status(thm)],[lower_dimension2]),[]).
% 
% cnf(157495064,plain,(between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)),inference(resolution,[status(thm)],[157487696,149674072]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[149677696,157495064]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------