%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GEO036-3 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art05.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 11:53:25 EDT 2009

% Result   : Unsatisfiable 10.7s
% Output   : Refutation 10.7s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   17 (  11 unt;   0 def)
%            Number of atoms       :   27 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   20 (  10   ~;  10   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   19 (   4 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t3,plain,
    ! [A,B] : between(A,B,B),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO036-3.tptp',unknown),
    [] ).

cnf(167562952,plain,
    between(A,B,B),
    inference(rewrite,[status(thm)],[t3]),
    [] ).

fof(t2,plain,
    ! [A,B] : between(A,A,B),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO036-3.tptp',unknown),
    [] ).

cnf(167578152,plain,
    between(A,A,B),
    inference(rewrite,[status(thm)],[t2]),
    [] ).

fof(prove_axioms_points_are_distinct,plain,
    ( $equal(lower_dimension_point_2,lower_dimension_point_1)
    | $equal(lower_dimension_point_3,lower_dimension_point_2)
    | $equal(lower_dimension_point_3,lower_dimension_point_1) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO036-3.tptp',unknown),
    [] ).

cnf(167617872,plain,
    ( $equal(lower_dimension_point_2,lower_dimension_point_1)
    | $equal(lower_dimension_point_3,lower_dimension_point_2)
    | $equal(lower_dimension_point_3,lower_dimension_point_1) ),
    inference(rewrite,[status(thm)],[prove_axioms_points_are_distinct]),
    [] ).

fof(b1,plain,
    ! [A,B,C,D] :
      ( ~ between(A,B,C)
      | ~ $equal(C,A)
      | between(D,B,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO036-3.tptp',unknown),
    [] ).

cnf(167569088,plain,
    ( ~ between(A,B,C)
    | ~ $equal(C,A)
    | between(D,B,C) ),
    inference(rewrite,[status(thm)],[b1]),
    [] ).

cnf(175842880,plain,
    ( ~ $equal(B,A)
    | between(C,A,B) ),
    inference(resolution,[status(thm)],[167569088,167578152]),
    [] ).

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/GEO036-3.tptp',unknown),
    [] ).

cnf(167265320,plain,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    inference(rewrite,[status(thm)],[lower_dimension1]),
    [] ).

cnf(176748600,plain,
    ~ $equal(lower_dimension_point_3,lower_dimension_point_2),
    inference(resolution,[status(thm)],[175842880,167265320]),
    [] ).

cnf(176815016,plain,
    ( $equal(lower_dimension_point_2,lower_dimension_point_1)
    | $equal(lower_dimension_point_3,lower_dimension_point_1) ),
    inference(resolution,[status(thm)],[167617872,176748600]),
    [] ).

cnf(214748800,plain,
    $equal(lower_dimension_point_3,lower_dimension_point_1),
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[167578152,176815016,167265320,theory(equality)]),
    [] ).

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/GEO036-3.tptp',unknown),
    [] ).

cnf(167269480,plain,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    inference(rewrite,[status(thm)],[lower_dimension2]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[167562952,214748800,167269480,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 10 seconds
% START OF PROOF SEQUENCE
% fof(t3,plain,(between(A,B,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO036-3.tptp',unknown),[]).
% 
% cnf(167562952,plain,(between(A,B,B)),inference(rewrite,[status(thm)],[t3]),[]).
% 
% fof(t2,plain,(between(A,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO036-3.tptp',unknown),[]).
% 
% cnf(167578152,plain,(between(A,A,B)),inference(rewrite,[status(thm)],[t2]),[]).
% 
% fof(prove_axioms_points_are_distinct,plain,($equal(lower_dimension_point_2,lower_dimension_point_1)|$equal(lower_dimension_point_3,lower_dimension_point_2)|$equal(lower_dimension_point_3,lower_dimension_point_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO036-3.tptp',unknown),[]).
% 
% cnf(167617872,plain,($equal(lower_dimension_point_2,lower_dimension_point_1)|$equal(lower_dimension_point_3,lower_dimension_point_2)|$equal(lower_dimension_point_3,lower_dimension_point_1)),inference(rewrite,[status(thm)],[prove_axioms_points_are_distinct]),[]).
% 
% fof(b1,plain,(~between(A,B,C)|~$equal(C,A)|between(D,B,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO036-3.tptp',unknown),[]).
% 
% cnf(167569088,plain,(~between(A,B,C)|~$equal(C,A)|between(D,B,C)),inference(rewrite,[status(thm)],[b1]),[]).
% 
% cnf(175842880,plain,(~$equal(B,A)|between(C,A,B)),inference(resolution,[status(thm)],[167569088,167578152]),[]).
% 
% fof(lower_dimension1,plain,(~between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO036-3.tptp',unknown),[]).
% 
% cnf(167265320,plain,(~between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)),inference(rewrite,[status(thm)],[lower_dimension1]),[]).
% 
% cnf(176748600,plain,(~$equal(lower_dimension_point_3,lower_dimension_point_2)),inference(resolution,[status(thm)],[175842880,167265320]),[]).
% 
% cnf(176815016,plain,($equal(lower_dimension_point_2,lower_dimension_point_1)|$equal(lower_dimension_point_3,lower_dimension_point_1)),inference(resolution,[status(thm)],[167617872,176748600]),[]).
% 
% cnf(214748800,plain,($equal(lower_dimension_point_3,lower_dimension_point_1)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[167578152,176815016,167265320,theory(equality)]),[]).
% 
% fof(lower_dimension2,plain,(~between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO036-3.tptp',unknown),[]).
% 
% cnf(167269480,plain,(~between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)),inference(rewrite,[status(thm)],[lower_dimension2]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[167562952,214748800,167269480,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------