%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GEO018-2 : 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 11:52:35 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   12 (   8 unt;   0 def)
%            Number of atoms       :   18 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   14 (   8   ~;   6   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-4 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   22 (   0 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(transitivity_for_equidistance,plain,
    ! [A,B,C,D,E,F] :
      ( ~ equidistant(A,B,C,D)
      | ~ equidistant(A,B,E,F)
      | equidistant(C,D,E,F) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-2.tptp',unknown),
    [] ).

cnf(147159536,plain,
    ( ~ equidistant(A,B,C,D)
    | ~ equidistant(A,B,E,F)
    | equidistant(C,D,E,F) ),
    inference(rewrite,[status(thm)],[transitivity_for_equidistance]),
    [] ).

fof(u_to_v_equals_w_to_x,plain,
    equidistant(u,v,w,x),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-2.tptp',unknown),
    [] ).

cnf(147381832,plain,
    equidistant(u,v,w,x),
    inference(rewrite,[status(thm)],[u_to_v_equals_w_to_x]),
    [] ).

cnf(155455848,plain,
    ( ~ equidistant(u,v,A,B)
    | equidistant(w,x,A,B) ),
    inference(resolution,[status(thm)],[147159536,147381832]),
    [] ).

fof(reflexivity_for_equidistance,plain,
    ! [A,B] : equidistant(A,B,B,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-2.tptp',unknown),
    [] ).

cnf(147150816,plain,
    equidistant(A,B,B,A),
    inference(rewrite,[status(thm)],[reflexivity_for_equidistance]),
    [] ).

cnf(155492160,plain,
    equidistant(w,x,v,u),
    inference(resolution,[status(thm)],[155455848,147150816]),
    [] ).

cnf(155215560,plain,
    ( ~ equidistant(A,B,C,D)
    | equidistant(C,D,B,A) ),
    inference(resolution,[status(thm)],[147159536,147150816]),
    [] ).

fof(prove_symmetry,plain,
    ~ equidistant(v,u,x,w),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-2.tptp',unknown),
    [] ).

cnf(147389712,plain,
    ~ equidistant(v,u,x,w),
    inference(rewrite,[status(thm)],[prove_symmetry]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[155492160,155215560,147389712]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(transitivity_for_equidistance,plain,(~equidistant(A,B,C,D)|~equidistant(A,B,E,F)|equidistant(C,D,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-2.tptp',unknown),[]).
% 
% cnf(147159536,plain,(~equidistant(A,B,C,D)|~equidistant(A,B,E,F)|equidistant(C,D,E,F)),inference(rewrite,[status(thm)],[transitivity_for_equidistance]),[]).
% 
% fof(u_to_v_equals_w_to_x,plain,(equidistant(u,v,w,x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-2.tptp',unknown),[]).
% 
% cnf(147381832,plain,(equidistant(u,v,w,x)),inference(rewrite,[status(thm)],[u_to_v_equals_w_to_x]),[]).
% 
% cnf(155455848,plain,(~equidistant(u,v,A,B)|equidistant(w,x,A,B)),inference(resolution,[status(thm)],[147159536,147381832]),[]).
% 
% fof(reflexivity_for_equidistance,plain,(equidistant(A,B,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-2.tptp',unknown),[]).
% 
% cnf(147150816,plain,(equidistant(A,B,B,A)),inference(rewrite,[status(thm)],[reflexivity_for_equidistance]),[]).
% 
% cnf(155492160,plain,(equidistant(w,x,v,u)),inference(resolution,[status(thm)],[155455848,147150816]),[]).
% 
% cnf(155215560,plain,(~equidistant(A,B,C,D)|equidistant(C,D,B,A)),inference(resolution,[status(thm)],[147159536,147150816]),[]).
% 
% fof(prove_symmetry,plain,(~equidistant(v,u,x,w)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO018-2.tptp',unknown),[]).
% 
% cnf(147389712,plain,(~equidistant(v,u,x,w)),inference(rewrite,[status(thm)],[prove_symmetry]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[155492160,155215560,147389712]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------